Fisher won't coach the Seminoles against Louisiana Monroe on Saturday. Associate head coach and defensive tackles coach Odell Haggins instead will lead the team.
"Coach Fisher did an exceptional job as both an assistant coach at FSU and in the challenging role of successor to the legendary Bobby Bowden," Florida State president John Thrasher said in a statement. "I believe Texas A&M is getting one of the best coaches in college football."
Fisher, 52, had hoped to wait to announce his decision until after Saturday's regular-season finale, which the Seminoles (5-6, 3-5 ACC) need to win to extend their streak of 35 consecutive bowl games. The game was postponed from Sept. 9 and rescheduled to Saturday because of Hurricane Irma.
Sources told ESPN that Texas A&M officials have approved a 10-year, $75 million, fully guaranteed contract for Fisher, which is the richest deal in college football history in terms of total value. He will be the second-highest-paid coach in the FBS with an average salary of $7.5 million, which ranks behind only Alabama's Nick Saban.
Fisher had signed an extension through 2024 with Florida State in December 2016 that gave him a base salary of $5.5 million. His buyout from Florida State is the sum remaining on the contracts of his assistants who are not retained, which would be in the range of $5 million to $7 million.
The Aggies will pay Fisher more than double what they paid former coach Kevin Sumlin, who made $35.5 million over six years, including his buyout.
Saban, who has guided the Crimson Tide to four national championships in 11 seasons, agreed to an eight-year contract extension in May that will pay him $65 million over the life of the deal. Saban is being paid $11.1 million this year and an annual average of $8.1 million.
Clemson coach Dabo Swinney is now the third-highest-paid coach in the FBS, at an average of $6.75 million over eight years.
"Obviously, he feels like it's the right move for him. I don't know," Swinney said when told of the move during a news conference for the ACC championship game. "I know he did an unbelievable job at Florida State. This is a business that's very public, as we all know, and from time to time, you have to make decisions. ... I like Jimbo. It's been a great, competitive journey. I've known him forever, when I was at Alabama and he was at Auburn.
"Florida State is Florida State. They'll hire a great coach. I don't have any doubt about that. And I guess we'll see [Fisher] next year, if that's what he's going to do. We play Texas A&M the next two years. If he is [going to the Aggies], I can't get rid of him. He'll still be a thorn in our side."
When Texas A&M fired Sumlin on Sunday, athletic director Scott Woodward stated a desire to compete for SEC and national championships. Asked Thursday what he would be looking for in a coach, university chancellor John Sharp deadpanned, "Nothing serious, just want him to win a national championship."
Sumlin went 51-26 in six seasons with the Aggies. Texas A&M must pay Sumlin a $10.4 million buyout by Jan. 25, and his buyout will not be reduced if he takes another coaching job.
Florida State said in its statement Friday that it would "move quickly" to evaluate candidates for the coaching position. ESPN reported last week that several Florida State officials expected Fisher to leave and have been preparing to target his replacement. Sumlin, Oregon's Willie Taggart, South Florida's Charlie Strong and Virginia Tech's Justin Fuente are options who might be considered.
ESPN reported Wednesday that Oregon offered Taggart a new contract worth more than $20 million, before incentives, over the next five years. A source told ESPN's Heather Dinich on Friday that Taggart has yet to sign the deal. Taggart tweeted that his agent is looking over the offer.
Fisher won the BCS National Championship in 2013 with the Seminoles and was 83-23 in eight seasons as their head coach.
Texas A&M last won a conference championship in 1998, when the Aggies were members of the Big 12. The school's lone national championship came in 1939.
Information from ESPN's Mark Schlabach, Chris Low and Sam Khan Jr. and The Associated Press was used in this report.