Briles resigned after Houston suffered a record-tying 56-point defeat to Army in the Armed Forces Bowl on Saturday.
Briles, the son of former Houston and Baylor coach Art Briles, agreed to a new three-year deal with Houston earlier this month. Briles agreed to the new deal at Houston after being a top candidate for the head coach job at Texas State, according to sources. The Houston Chronicle reported the contract made Briles the highest-paid assistant coach at a non-Power 5 school.
That revised contract at Houston delayed the move to Florida State, which had been likely for several weeks.
Briles began his coaching career on his father's Baylor staff in 2008 and remained there until 2016, serving as offensive coordinator and quarterbacks coach the final two seasons. He spent the 2017 season as offensive coordinator and quarterbacks coach on Lane Kiffin's staff at Florida Atlantic, which won a Conference USA championship.
At Florida State, he will replace Walt Bell, who left to take the head-coaching position at UMass.
Entering Saturday's bowl games, Houston (8-5) ranked fourth in the nation with 46.4 points per game and sixth with 529 yards per game. The Cougars' 44 passing touchdowns were third-most in FBS.
Houston's season ended in a tailspin, as it lost its fourth game in the past five and was limited to just 14 points against Army. The Cougars' previous lowest point total of the season was 31 in losses at SMU on Nov. 3 and Memphis in the regular-season finale.