Michigan and its retiring coach will play No. 9 Florida in the Capital One Bowl in Orlando on New Year's Day.
The Gators (9-3) won four consecutive games to end the season and were chosen ahead of Southeastern Conference Eastern Division champion Tennessee in the league's bowl pecking order.
The Wolverines (8-4) could have secured a spot in the Rose Bowl by beating rival Ohio State two weeks, but they lost 14-3 and Carr announced his retirement the following day.
Michigan is still looking for its next coach after LSU coach Les Miles agreed to stay with on Saturday.
Regardless of when the search wraps up, Carr already agreed to stay with the team through its bowl game.
Now, Carr can only hope for better results against Florida than what the Buckeyes had in January. The Gators romped 41-14 in the Bowl Championship Series national title game.
That was Florida's second national title.
Carr won one in 1997, but that seemed like a distant memory after Michigan's shocking loss to Appalachian State to open the year and after Carr fell to 6-7 against Ohio State. He also dropped to 1-6 against Jim Tressel-coached teams.
Michigan has lost its last four bowl games. The last win came against Florida in the 2003 Outback Bowl, a 38-30 victory that was highlighted by one of the worst coaching decisions in former Florida coach Ron Zook's career.
Driving for a possible tying score with time dwindling, Zook OK'd a play that called for receiver Vernell Brown to take a handoff and try to throw downfield to quarterback Rex Grossman. It failed. Michigan intercepted the pass and Grossman, unbelievably, wrapped up his college career running a pass pattern instead of throwing a pass.
The Gators have won both of their bowl games under coach Urban Meyer, beating Iowa 31-24 in the 2006 Outback Bowl and then winning it all in Glendale, Ariz., last season.