Joseph, who interviewed for the Broncos' head-coaching job in 2015 when the team hired Gary Kubiak, is the team's choice to be the 16th coach in franchise history, it was announced Wednesday.
The deal is for four years, and Joseph will be introduced at a news conference on Thursday.
Joseph, 44, just finished his first season as the Miami Dolphins' defensive coordinator.The Dolphins were defeated 30-12 by thePittsburgh Steelersin the wild-card round Sunday.
"Becoming head coach of the Denver Broncos is a dream job for many reasons," Joseph said in a statement Wednesday. "The Broncos have an unbelievable winning tradition and great fan support. But what makes this even more special is it's a place that's ready to win. This is not a rebuilding situation -- It's a reboot. There is a culture of winning here, and the standards around here won't change -- Those are to win championships.
"I am very thankful to John Elway and Joe Ellis for this opportunity. It's incredibly humbling to be part of an organization like the Broncos with so much history and success, especially when you see all the great things this franchise has accomplished."
The Broncos had vetted Joseph long before this week, as he interviewed for the job in 2015. Many with the Broncos say he would have been the pick back then had Kubiak not become available.
Joseph becomes the sixth black active head coach in the NFL, joining Mike Tomlin (Steelers), Marvin Lewis (Bengals), Hue Jackson (Browns), Jim Caldwell (Lions) and Todd Bowles (Jets).
Kubiak announced at the end of the season that he was stepping away from coaching because of health issues. Broncos executive vice president of football operations/general manager John Elway started the team's search for a new coach that same day.
The Broncos interviewed Kansas City Chiefs special teams coordinator Dave Toub on Friday and Atlanta Falcons offensive coordinator Kyle Shanahan, but the Broncos could not get a deal done with either until those teams were out of the playoffs or after the Super Bowl.
"During this process, we were very fortunate to spend time with three very qualified candidates who all could have been the next head coach of our team," Elway said in a statement Wednesday. "For us, Vance Joseph is the best fit to become the head coach of the Denver Broncos.
"Vance is very good football coach and teacher who is ready for this opportunity. His leadership qualities, his vision for building a championship team and his ability to get the most out of players are off the charts. In talking with Vance, the culture that he believes in and the culture of our organization are closely aligned and focused on one thing: Winning. He understands the high expectations this franchise has always had under (owner) Pat Bowlen, and he embraces them."
Joseph arrived Tuesday for his interview and dinner with team officials. He then stayed and was back at the team's suburban Denver complex Wednesday morning as the contract was finalized. He canceled a scheduled interview Wednesday with the San Diego Chargers.
Sources within the team said if Joseph could adequately address how he would repair the Broncos' offense, he would edge Shanahan for the job.
The Broncos have scheduled interviews with offensive coordinator candidates Mike McCoy and Bill Musgrave on Thursday, sources told ESPN NFL Insider Adam Schefter.
Joseph is a former University of Colorado player and assistant coach -- he was a former college teammate of the Broncos' current director of player personnel Matt Russell, who was one of the Broncos' front-office executives to sit in on the team's interviews with Shanahan, Toub and Joseph.
Joseph will inherit a 9-7 team that missed the playoffs for the first time since 2010 but includes three first-team All-Pro players on defense in cornerbacks Chris Harris Jr. and Aqib Talib as well as linebacker Von Miller.
The Broncos are expected to be almost $40 million under the salary cap for the 2017 season and could have as many as 10 draft picks after compensatory picks are handed out in March. This season ended a streak of five consecutive division titles for the Broncos; the team won at least 12 games in four of those seasons, made two Super Bowl trips and won Super Bowl 50 last February.
Elway said throughout the search that he was looking for a "young" and "bright" coach for the job. And after Joseph's interview Wednesday, Elway took to Twitter to say: "He has great leadership qualities and a strong vision of what it takes to win."
Joseph was on Kubiak's staff with the Houston Texans as well as defensive backs coach for the Cincinnati Bengals for three seasons before he was hired by former Broncos offensive coordinator Adam Gase to be the Dolphins' defensive coordinator this past season.
This year was the first in the Dolphins' roster makeover, and the defense had several injuries to starters. As a result, the Dolphins finished 29th in total defense, 18th in scoring defense.
"He's done a great job with our players; I can speak for that first hand," Gase said Wednesday. "He took so much off of my plate, where I never had to worry about anything with the defense. He really did a great job with all those guys in that room. He did a great job directing those guys, and he really made my life a lot easier than it would've, could've been."
Joseph was part of the Texans' staff under Wade Phillips when Houston had the league's No. 2 defense in 2011 and No. 7 defense in 2012. Joseph's hire brings some uncertainty to Phillips' status as Denver's defensive coordinator given Joseph might want to call plays on defense.
Phillips' contract with the team is up.
"I guess everybody needs something new on the offensive side," Broncos cornerback Chris Harris Jr. told ESPN's Josina Anderson on Wednesday. "Defensive side, I think he is very similar to Wade...He's coached under Wade. Right there, I think he will fit right in.
"I don't know too much about Vance Joseph. But from all the Texans players I have talked to, they said he was great coach and they still love him. ... Also, when you talk to guys around the league, there is nothing negative about him."
Joseph's players have routinely praised him for his ability to communicate expectations and game plans, and the Bengals' Lewis has consistently praised Joseph as a future head coach.
"In today's world, obviously we want someone that's very smart and bright. I think in today's world when dealing with players, it's a different game now than it used to be. There's a lot more to that as far as dealing with the different personalities and kids today," Elway said last week.
"So much of it is the relationship that goes on that goes on in that locker room, the relationship they have with the head coach and the effort that's put out there. If you know how to motivate a football team and to be able to be on the same page with a football team, I think is as important.
"Obviously you want a guy that can manage people and understand what he wants to do on the offensive side as well as the defensive side but also can manage coaches and manage players, which I think is the biggest part of that job."
ESPN's James Walker contributed to this report.