Omar Kelly of the Sun Sentinel initially reported the news.
Andrew Abramson of the Palm Beach Post reported Bo Hardegree has been named quarterback coach and Jermiah Washburn has been named assistant offensive line coach.
Christensen spent the past 14 years with the Colts in various positions. He served as the team's offensive coordinator in 2010 and 2011 before becoming the quarterbacks coach in 2012.
Christensen's other roles with the Colts included wide receivers coach (2002-09) and assistant head coach (2008-09). He was around for the glory days of Peyton Manning, coaching in the playoffs in 12 of his 14 years. During the Colts' Super Bowl XLI win over the Chicago Bears, he was in charge of the receivers.
Colts head coach Chuck Pagano is going to miss having him on the sidelines in Indianapolis, per Colts reporter Heather Lloyd:
Clyde Christensen, who Chuck Pagano called "the best quarterbacks coach in the history of the NFL" is going to the Dolphins as OC.— The Blue Mare (@TheBlueMare) January 17, 2016
Christensen will pair with newly hired head coach Adam Gase as he tries to revive a Dolphins offense that ranked 27th in the NFL in scoring last year with just 19.4 points per game.
According to James Walker of ESPN.com, it will be a slow transition for Christensen, as Gase plans to handle the play-calling.
After working with the likes of Manning and Andrew Luck, Christensen will have Ryan Tannehill under center after a disappointing end to his season that saw him throw just four touchdowns in his final five games.