The Giants said Tuesday that family friends informed them of his death.
Son John Fassel, special teams coordinator of the Dallas Cowboys, confirmed the death to the Los Angeles Times. He told the newspaper his father was taken to a Las Vegas hospital with chest pains and died while being treated Monday.
"Is is with a very heavy heart to announce that we lost our Dad yesterday," John Fassel said in a statement Tuesday. "... While our Dad will be remembered as a long time face and fan in the football world, his legacy will live forever in our hearts as the greatest Dad and Grandpa of all time."
Jim Fassel, the 1997 NFL Coach of the Year, guided the Giants from 1997 to 2003, posting a 58-53-1 record. He was 2-3 in the postseason, including a 34-7 loss to the Baltimore Ravens in the Super Bowl in February 2001.
Fassel's 58 victories place him behind Steve Owen (153), Tom Coughlin (102) and Bill Parcells (77) among Giants coaches. Owen and Parcells are Hall of Famers, and Parcells and Coughlin each won two Super Bowls.
Fassel coached a number of outstanding players for the Giants, including Hall of Famer Michael Strahan. Strahan, now a co-host of "Good Morning America'' and a television personality, called Fassel a big part of his life.
"Just a great man, great coach, and he will be missed,'' said the former defensive end, who sent condolences to the Fassel family during Tuesday's GMA broadcast.
"I enjoyed every minute with him as my coach and after my career when we continue to stay in touch and talk,'' Strahan said.
Former Giants running back Tiki Barber was among those to pay tribute to Fassel on Twitter, writing, "He challenged me to excel at the small things, then allowed me run with the big ones."
Current Giants coach Joe Judge spoke of Fassel's ties to the team during minicamp Tuesday.
"That's something that makes you kind of sit back and reflect. It brings up a lot of great coaches who have been through here,'' Judge said. "Look, it's definitely an honor to be in the same position as all of these coaches.''
Fassel was born in Anaheim, California, on Aug. 31, 1949. He played quarterback at Fullerton College, USC and Long Beach State. In 1972, he was drafted in the seventh round by the Chicago Bears. He played briefly in the NFL and World Football League.
Fassel was considered an offensive expert and worked for the Giants as offensive coordinator in 1991 and '92. He was the coordinator with the Denver Broncos, Oakland Raiders and Arizona Cardinals before returning to New York as head coach after Dan Reeves was fired.
Taking over in 1997, Fassel inherited a team that had missed the playoffs five of the previous six seasons under Ray Handley and Reeves. He quickly turned things around, posting a 10-5-1 mark and leading New York to the NFC East title, its first since winning the Super Bowl under Parcells in February 1991.
The Giants missed the playoffs the following two seasons. They appeared headed to the postseason in 2000 after opening with a 7-2 record, but consecutive losses to St. Louis and Detroit in November had many thinking the team was going to fold.
Fassel had other ideas. On Nov. 22, four days before a game with Arizona, the coach put his reputation on the line, telling the media to target him.
"I'll take full responsibility. I'm raising the stakes right now,'' he said. "This is a poker game, I'm shoving my chips to the middle of the table, I'm raising the ante. Anybody wants in, get in. Anybody wants out, get out. This team is going to the playoffs. OK. This team is going to the playoffs."
The Giants crushed Arizona 31-7 and finished the regular season on a five-game winning steak that gave them the NFC East title with a 12-4 record. Playoff wins over Philadelphia and Minnesota followed before the Ravens crushed them in the Super Bowl.
New York missed the playoffs in 2001 and made it as a wild card in 2002, but Fassel lost the team in 2003 and announced two games before the end of the season he would not be returning.
"On behalf of the Mara and Tisch families and our entire organization, I would like to express our condolences to the Fassel family and Jim's friends. We were all saddened to hear of Jim's passing. Jim was a good man and his record as our coach speaks for itself," Giants co-owner John Mara said in a statement. "Jim distinguished himself by the way he managed our team and devoted his efforts to the fire fighters and other families following the tragedy of 9-11. The players respected Jim and enjoyed playing for him and his coaching staff. And we appreciated his seven years of leading our team."
Coughlin was hired and led the Giants to Super Bowls after the 2007 and 2011 seasons.
Fassel played college football before a brief career in the NFL and Canadian football. He was also part of the coaching staffs at Denver, Oakland, Arizona and Baltimore, as well as head coach at the University of Utah. He never served as a head coach in the NFL again, but was the head man for the United Football League's Las Vegas Locomotives.
Fassel joined Westwood One radio as a color commentator for its Sunday NFL games in 2007. He stayed with the network for two seasons, calling Sunday afternoon games with Harry Kalas and "Sunday Night Football'' with Dave Sims. Fassel was also part of Westwood One's playoff coverage those two years, calling various games, and worked the 2007 and 2008 NFC Championship Games.
John Fassel will not be at the Cowboys' minicamp this week following his father's death. Fassel's assistant, Matt Daniels, will run the special teams' portions of practice.
"John's as big of a family man as we have here, and our heart goes out to him and his family right now," Cowboys coach Mike McCarthy said. "John's love for his family and especially his father, Jim, he's shared many stories just in our short time together."
ESPN's Todd Archer and The Associated Press contributed to this report.
Remembering Jim Fassel
Adam Schefter and Ryan Clark share their memories of Jim Fassel, who has died at 71.