"Coach Fox is a great fit for us not only with his coaching ability but also with his personality. He's a dynamic and proven leader," John Elway, Broncos executive vice president of football operations, said in a statement.
"He's coached great defenses, turned teams around and been to Super Bowls. We couldn't be more excited to have him lead our football team."
While Fox exited Carolina on a disappointing note, he did go 73-71 over nine regulars seasons and guided the Panthers to the Super Bowl in his second season in charge.
"The Broncos have a culture of winning, and I am excited to continue that legacy," said Fox, who will be introduced at a news conference on Friday. "I can't wait to get to work."
But turning a team around is something Fox has experience in.
He took over a Carolina team in 2002 that had gone 1-15 and led the Panthers to a 7-9 record in his first season, one of the best turnarounds by a first-year an NFL coach.
In 2003 the Panthers improved to 11-5 and claimed the NFC South crown en route to the Super Bowl where they lost to the New England Patriots.
(Writing by Steve Keating in Toronto; editing by Frank Pingue)