Fisher won't coach in the Seminoles' game against Louisiana-Monroe on Saturday.
However, despite being ranked No. 3 heading into this season, Florida State has just five wins and is merely aiming to become bowl eligible.
ESPN reported last week that several Florida State officials expected Fisher to leave and have been preparing to target his replacement. He is the first coach since Johnny Majors left Pitt for Tennessee back in 1977 to leave a school he won a national championship at for another school.
One former FSU quarterback, Danny Kanell, tweeted, reminding Florida State to be thankful for the years Jimbo spent here and to get excited for the future. He succeeded Bobby Bowden in 2010.
"I don't know", Swinney said, when told of the move during a news conference for the ACC championship game. "I wish him the very best".
"Florida State is Florida State".
"President Thrasher and I have worked together through this challenging period while coach Fisher was making a decision, and I appreciate the cooperation, support and leadership he has provided", athletic director Stan Wilcox said. They'll hire a great coach. And I guess we'll see [Fisher] next year, if that's what he's going to do. I don't have any doubt about that.
Texas A&M has invested heavily in facilities the past five years, including a football operations center. The top name so far has been first-year OR coach Willie Taggart, who took over at OR last offseason after turning around the South Florida program. The school's lone national championship came in 1939.
Fisher was 83-23 in his eight seasons in Tallahassee, including one national title that he won with Jameis Winston in 2013.
Information from ESPN's Mark Schlabach and Sam Khan Jr. and The Associated Press was used in this report.