Fisher, who led Florida State to a national championship in 2013, resigned on Friday from coaching the Seminoles after eight seasons to join the Aggies.
The 52-year-old Fisher was introduced by Texas A&M athletic director Scott Woodward during a news conference in College Station.
"I know I come in here with great expectations," Fisher said. "We're going to be driven to be the very best every day. We're going to strive for excellence every day."
No state-appropriated funds will be used to pay the coach's salary, the school announced. Fisher made $5.7 million this season at Florida State as part of an extension he signed in December 2016.
"It was a no-brainer," Fisher said Monday morning of his decision.
Fisher grew frustrated with Florida State officials over the failure to improve football facilities.
"You can have the greatest coaches in the world, but if your administration doesn't see things in the way you see things, and allow you to do things that way, nothing can be achieved," Fisher said. "There's a oneness to everything you to do be successful, and I knew he had the same vision I did."
Texas A&M fired Kevin Sumlin on Nov. 26, one day after the Aggies ended their regular season with a 7-5 mark following a 45-21 setback to LSU. Sumlin went 51-26 in six seasons as coach.
Fisher had an 83-23 with the Seminoles and won the 2013 BCS national championship with a 14-0 record.
"I had no plans of ever leaving there," Fisher said. "As I researched, I thought it was an opportunity I couldn't pass up and a challenge out there I just couldn't pass up."
Fisher acknowledged the challenge of the Southeastern Conference West division, which includes Alabama, Auburn and LSU.
Texas A&M, which moved to the SEC in 2012, is 25-23 in the conference, including 19-21 since going 6-2 in its first season.
"I understand this league. I grew up in this league," said Fisher, who was an assistant at LSU (2000-06) and Auburn (1993-98). "We understand everything that goes with it. I want to take Texas A&M somewhere they haven't been and that's the champions of the SEC and then a national championship. I think all the ingredients are here."
Fisher took over the FSU football program in 2010, following the retirement of coaching legend Bobby Bowden.
"There are very few places in America that I would have left Florida State for, and Texas A&M is at the top," Fisher said in an earlier statement. "I want to thank the great people at Florida State for an incredible opportunity.
"President (Michael) Young and (athletic director) Scott Woodward have been tremendous in our discussions and I know that we will do great things together. We have everything in place to reach our goal, which is to bring a national title to College Station, and I can't wait to get started."
Fisher averaged more than 10 wins per season during his tenure at Florida State and his .783 winning percentage was fourth-best among active head coaches (minimum five years) and the best in Atlantic Coast Conference. Fisher's ACC record was 48-16 with three conference championships.
"When we set out to find a new leader of our proud football program, we set our sights high. Jimbo is among the best football coaches in America and a perfect fit for A&M," Woodward said in a statement. "His experience in the Southeastern Conference; his knowledge of the game; his recruiting acumen, and his management skills will allow him to achieve the highest levels of success when matched with what A&M offers. We are thrilled to welcome Jimbo to the Aggie Family."
Fisher will not coach in the Aggies' Belk Bowl game against Wake Forest in Charlotte, N.C., on Dec. 29. Texas A&M assistant Jeff Banks will serve as the interim coach.