Although the school hasn't announced the move, Crimson Tide coach Nick Saban said in a Monday news conference that FAU had "made a great hire."
"We think this is a wonderful opportunity for him to be a head coach again," Saban said. "I think FAU has selected someone that is going to do a great job for them. He's done a great job here molding our offensive players to what they can do to have the best chance to be successful, and I think that's always something that's very telling about the quality of a coach."
Kiffin had been engaging in back-and-forth talks with the Conference USA school since last Friday, sources told ESPN. At one point, negotiations between the two sides stalled, but a deal was struck early Monday morning, sources said.
Kiffin will remain Alabama's offensive coordinator throughout the College Football Playoff, Saban said, maintaining a similar role to former defensive coordinator Kirby Smart's last season, after he took Georgia's head-coaching job.
Kiffin, 41, returns to the head-coaching fraternity after three seasons as offensive coordinator under Saban. The Crimson Tide are in pursuit of their second straight national championship and have won three straight SEC titles, with Kiffin getting three different first-year starters ready at quarterback, including true freshman Jalen Hurts this season.
Kiffin's contract with Alabama was set to expire after this season, and he wasn't expected to return, which helps explain why he made a hard push to find a head-coaching job -- even if it meant a step down in prestige and most likely a pay cut.
"Lane appreciates the opportunity Nick Saban gave him and feels good about everything Alabama accomplished during his three years there, but he was at a point in his career where he was ready to go prove that he could be a head coach again," a source close to the situation told ESPN.com.
Kiffin's salary at FAU will average in the $1 million range annually, according to sources. He was making $1.4 million per year as Alabama's offensive coordinator.
One of the finalists for the Houston head-coaching job, which went to Major Applewhite last week, Kiffin takes over an FAU program that went 3-9 this past season. He replaces Charlie Partridge, who was fired in November after going 9-27 in three seasons at the Boca Raton, Florida, school.
Kiffin was also being pursued by new LSU head coach and friend Ed Orgeron to be the Tigers' offensive coordinator. But Kiffin wanted to keep all of his options open, including going back to the NFL.
Considered by many to be one of the top offensive minds in the game, Kiffin has generated his share of controversy in his career, which has given some athletic directors and presidents around the country cause for concern about his ability to manage a program. But Saban said last week that he is confident Kiffin is ready to be a head coach again.
This will be Kiffin's fourth head-coaching stint. He was the Oakland Raiders' head coach for the 2007 season and part of the 2008 season before being fired by Al Davis, the late Raiders owner. He went to Tennessee as head coach in 2009, but he bolted for USC after just one season in Knoxville.
A former assistant at USC under Pete Carroll, Kiffin was the Trojans' head coach from 2010 to '12 and then was fired five games into the 2013 season by then-USC athletic director Pat Haden. At USC, Kiffin inherited a program under severe NCAA sanctions. He was 35-21 at Tennessee and USC and 5-15 with the Raiders. He landed all three head-coaching jobs before the age of 35.
Kiffin has some ties to the Florida area. His father, Monte Kiffin, was the Tampa Bay Buccaneers' defensive coordinator for 13 years from 1996 to 2008, and Lane Kiffin was on the Jacksonville Jaguars' staff for a season in 2000.