The university said Wooden died Friday night of natural causes at Ronald Reagan UCLA Medical Center, where he had been hospitalized since May 26.
Jim Wooden and Nancy Muehlhausen issued a statement shortly after their father died, saying, "He has been, and always will be, the guiding light for our family.
"The love, guidance and support he has given us will never be forgotten. Our peace of mind at this time is knowing that he has gone to be with our mother, whom he has continued to love and cherish."
They thanked well-wishers for their thoughts and prayers and asked for privacy.
With his signature rolled-up game program in hand, Wooden led the Bruins to 10 NCAA championships, including an unmatched streak of seven in a row from 1967 to 1973.
Over 27 years, he won 620 games, including 88 straight during one historic stretch, and coached many of the game's greatest players such as Bill Walton and Lew Alcindor - later known as Kareem Abdul-Jabbar.
"It's kind of hard to talk about Coach Wooden simply, because he was a complex man. But he taught in a very simple way. He just used sports as a means to teach us how to apply ourselves to any situation," Abdul-Jabbar said in a statement released through UCLA.
"He set quite an example. He was more like a parent than a coach. He really was a very selfless and giving human being, but he was a disciplinarian. We learned all about those aspects of life that most kids want to skip over. He wouldn't let us do that."
Wooden is the only person to be inducted into the Basketball Hall of Fame as both a player and a coach.
"He was always the boss. He always knew what to say," former UCLA star Jamaal Wilkes told the Associated Press. "Even in the heyday of winning and losing, you could almost discuss anything with him. He always had that composure and wit about him. He could connect with all kind of people and situations and always be in control of himself and seemingly of the situation."
Walton and Wilkes were among former players who visited Wooden in the hospital this week. Wilkes came twice and said Wooden recognized him and that the coach's mind was "sharp as a tack" until the end although his body was "very, very frail."
Wilkes said he recognized what he called "that little glint" in Wooden's pale blue eyes. He was in the room with Wooden's son when Wooden asked to be shaved.
"His son made the comment that when he got shaved he was getting ready to see Nellie," Wilkes said, referring to Wooden's late wife.
During his second visit Wednesday night, Wilkes asked Wooden if he recognized him.
"His glasses fogged up and he had to clean his glasses," Wilkes said. "He looked at me and said, 'I remember you, now go sit down."'
St. John's coach Steve Lavin followed a similar career path as Wooden, coaching seven years at UCLA after serving as an assistant at Purdue.
"Even though we anticipated this day, the finality still strikes with a force equal to a ton of bricks," Lavin said.
"There was the common affinity we shared for Purdue and UCLA and that forged a unique bond. I turned to him for perspective at every critical juncture over the past 20 years. Ninety-nine years of goodness and now he's back with Nell."
Wooden was a groundbreaking trendsetter who demanded his players be in great condition so they could play an up-tempo style not well-known on the West Coast at the time.
But his legacy extended well beyond that.
He was the master of the simple one- or two-sentence homily, instructive little messages best presented in his famous "Pyramid of Success," which remains must-read material, not only for fellow coaches but for anyone in a leadership position in American business.
He taught the team game and had only three hard-and-fast rules - no profanity, tardiness or criticizing fellow teammates. Layered beneath that seeming simplicity, though, were a slew of life lessons - primers on everything from how to put on your socks correctly to how to maintain poise: "Not being thrown off stride in how you behave or what you believe because of outside events."
"What you are as a person is far more important that what you are as a basketball player," was one of Wooden's key messages.
"There will never be another John Wooden," UCLA athletic director Dan Guerrero said. "This loss will be felt by individuals from all parts of society. He was not only the greatest coach in the history of any sport but he was an exceptional individual that transcended the sporting world. His enduring legacy as a role model is one we should all strive to emulate."
Wooden began his career as a teacher during the Great Depression and was still teaching others long past retirement. Up until about two years ago, he remained a fixture at UCLA games played on a court named after him and his late wife, Nell, and celebrated his 99th birthday with a book he co-authored on how to live life and raise children.
Asked in a 2008 interview the secret to his long life, Wooden replied: "Not being afraid of death and having peace within yourself. All of life is peaks and valleys. Don't let the peaks get too high and the valleys too low."
Asked what he would like God to say when he arrived at the pearly gates, Wooden replied, "Well done."
Even with his staggering accomplishments, he remained humble and gracious. He said he tried to live by advice from his father: "Be true to yourself, help others, make each day your masterpiece, make friendship a fine art, drink deeply from good books - especially the Bible, build a shelter against a rainy day, give thanks for your blessings and pray for guidance every day."
While he lived his father's words, many more lived his. Those lucky enough to play for him got it first hand, but there was no shortage of Wooden sayings making the rounds far away from the basketball court.
"Learn as if you were to live forever; live as if you were to die tomorrow," was one.
"Don't give up on your dreams, or your dreams will give up on you," was another.
Born Oct. 14, 1910, near Martinsville, Ind., on a farm that didn't have electricity or indoor plumbing, Wooden's life revolved around sports from the time his father built a baseball diamond among his wheat, corn and alfalfa. Baseball was his favorite sport, but there was also a basketball hoop nailed in a hayloft. Wooden played there countless hours with his brother, Maurice, using any kind of ball they could find.
He led Martinsville High School to the Indiana state basketball championship in 1927 before heading to Purdue, where he was All-America from 1930-32. The Boilermakers were national champions his senior season, and Wooden, nicknamed "the Indiana Rubber Man" for his dives on the hardcourt, was college basketball's player of the year.
But it wasn't until he headed west to Southern California that Wooden really made his mark on the game.
Wooden guided the Bruins to seven consecutive titles from 1967 through 1973 and a record 88-game winning streak in the early 1970s. From the time of his first title following the 1963-64 season through the 10th in 1974-75, Wooden's Bruins were 330-19, including four 30-0 seasons.
"My reaction is sadness yet at this point we have to celebrate maybe the most important guy in the history of the game," Connecticut coach Jim Calhoun told the AP. "There has been no greater influence on college basketball not just about the game but the team.
"He gave so much to basketball and education. In my opinion if he's not as important as Dr. Naismith, he's right next to him."
The bespectacled former high school teacher ended up at UCLA almost by accident. Wooden was awaiting a call from the University of Minnesota for its head coaching job and thought he had been passed over when it didn't come. In the meantime, UCLA called, and he accepted the job in Los Angeles.
Minnesota officials called later that night, saying they couldn't get through earlier because of a snowstorm, and offered him the job. Though Wooden wanted it more than the UCLA job, he told them he already had given UCLA his word and could not break it.
The Bruins were winners right away after Wooden took over as coach at UCLA's campus in Westwood in 1949, although they were overshadowed by Bill Russell and the University of San Francisco, and later Pete Newell's teams at California.
At the time, West Coast teams tended to play a slow, plodding style. Wooden quickly exploited that with his fast-breaking, well-conditioned teams, who wore down opponents with a full-court zone press and forever changed the style of college basketball.
Still, it would be 16 seasons before Wooden won his first NCAA championship with a team featuring Walt Hazzard that went 30-0 in 1964. After that, they began arriving in bunches, with top players such as Alcindor, Walton, Wilkes, Lucius Allen, Gail Goodrich, Marques Johnson, Michael Warren and Sidney Wicks coming to Westwood.
Each of Wooden's players would learn at the first practice how to properly put on socks and sneakers. Each would learn to keep his hair short and face clean-shaven, even though the fashions of the 1960s and '70s dictated otherwise.
And each would learn Wooden's "pyramid of success," a chart he used to both inspire players and sum up his personal code for life.
Industriousness and enthusiasm were its cornerstones; faith, patience, loyalty and self-control were some of the building blocks. At the top of the pyramid was competitive greatness.
"Be more concerned with your character than your reputation, because your character is what you really are, while your reputation is merely what others think you are," Wooden would tell them.
Wooden never had to worry about his reputation. He didn't drink or swear or carouse with other coaches on the road, though he did have a penchant for berating referees.
"Dadburn it, you saw him double-dribble down there!" went a typical Wooden complaint to an official. "Goodness gracious sakes alive!"
Wooden would coach 27 years at UCLA, finishing with a record of 620-147. He won 47 NCAA tournament games. His overall mark as a college coach was 885-203, an .813 winning percentage that remains unequaled.
"Many have called Coach Wooden the 'gold standard' of coaches. I believe he was the 'gold standard' of people and carried himself with uncommon grace, dignity and humility," Duke coach Mike Krzyzewski said. "Coach Wooden's name is synonymous with excellence, and deservedly so. He was one of the great leaders - in any profession - of his generation."
Wooden's legacy as a coach will always be framed by two streaks - the seven straight national titles UCLA won beginning in 1967 and the 88-game winning streak that came to an end Jan. 19, 1974, when Notre Dame beat the Bruins 71-70.
After the loss, Wooden refused to allow his players to talk to reporters.
"Only winners talk," he said. A week later, UCLA beat the Irish at home by 19 points.
A little more than a year later, Wooden surprisingly announced his retirement after a 75-74 NCAA semifinal victory over Louisville. He then went out and coached the Bruins for the last time, winning his 10th national title with a 92-85 win over Kentucky.
After that victory, Wooden walked into the interview room at the San Diego Sports Arena to face about 200 reporters, who let their objectivity slip and applauded.
"When I think of a basketball coach the only one I ever thought of was Coach Wooden. He had a great life and helped so many coaches until well in his 90s," Syracuse coach Jim Boeheim told The Associated Press. "Every time I talked to him he would give me some words of advice. He's the best of all time. There will never be another like him, and you can't say that about too many people."
The road to coaching greatness began after Wooden graduated with honors from Purdue and married Nell Riley, his high school sweetheart.
In a 2008 public appearance with Los Angeles Dodgers announcer Vin Scully, in which the men were interviewed in front of an audience, Wooden said he still wrote his late wife - the only girl he ever dated - a letter on the 21st of each month. "She's still there to me," he said. "I talk to her every day."
He coached two years at Dayton (Ky.) High School, and his 6-11 losing record the first season was the only one in his 40-year coaching career.
He spent the next nine years coaching basketball, baseball and tennis at South Bend (Ind.) Central High School, where he also taught English.
"I think the teaching profession contributes more to the future of our society than any other single profession," he once said. "I'm glad I was a teacher."
Wooden disliked the Wizard of Westwood nickname, preferring to be called coach.
"I'm no wizard, and I don't like being thought of in that light at all," he said in a 2006 interview with the UCLA History Project. "I think of a wizard as being some sort of magician or something, doing something on the sly or something, and I don't want to be thought of in that way."
Wooden served in the Navy as a physical education instructor during World War II, and continued teaching when he became the basketball coach at Indiana State Teachers College, where he went 47-17 in two seasons.
In his first year at Indiana State, Wooden's team won the Indiana Collegiate Conference title and received an invitation to the NAIB tournament in Kansas City. Wooden, who had a black player on his team, refused the invitation because the NAIB had a policy banning African Americans. The rule was changed the next year, and Wooden led Indiana State to another conference title.
It was then that UCLA called, though Wooden didn't take the job to get rich. He never made more than $35,000 in a season, and early in his career he worked two jobs to make ends meet.
"My first four years at UCLA, I worked in the mornings at a dairy from six to noon then I'd come into UCLA," he told The Associated Press in 1995. "Why did I do it? Because I needed the money. I was a dispatcher of trucks in the San Fernando Valley and was a troubleshooter. After all the trucks made their deliveries and came back, I would call in the next day's orders, sweep out the place and head over the hill to UCLA."
After he enjoyed great success at UCLA, the Los Angeles Lakers reportedly offered Wooden their head coaching job at a salary 10 times what he was making, but he refused.
Nell, Wooden's wife of 53 years, died of cancer in 1985. Besides his son and daughter, Wooden is survived by three grandsons, four granddaughters and 13 great-grandchildren.
Funeral services will be private. A public memorial will be held later, with a reception for former players and coaches.
AP Basketball Writer Jim O'Connell in New York contributed to this report.