Brennan said in a statement posted to social media that he is "stepping away from football."
"I am forever grateful for every opportunity I've been given, every obstacle I've overcome, and every second I've been a Tiger," he said in the statement. "However, after five seasons, it is time for me to start a new chapter in my life."
"We are grateful to Myles for everything he has done for LSU Football," LSU coach Brian Kelly said in a statement. "Myles is a great leader who has made a tremendous impact on this program, and he has earned the respect of everyone here through his commitment and love for LSU.
"Myles has always embodied the traits required to fulfill our mission to graduate champions, and we have full confidence those traits will help him succeed at every step in his journey as he moves forward."
Brennan briefly entered the transfer portal last winter when former LSU coach Ed Orgeron was fired.
After Kelly was hired from Notre Dame, he reached out to Brennan and persuaded him to return.
A few months later, Daniels entered the portal. Kelly told ESPN in the spring that he was hesitant to sign Daniels, calling it "one of the more difficult decisions that I made in the offseason."
"But it was about competition," Kelly said. "It was about upgrading the competition on this roster across the board."
A talented dual-threat quarterback, Daniels threw for 6,025 yards and 32 touchdowns in three seasons as a starter for the Sun Devils.
Brennan took equal reps with Daniels and Nussmeier during LSU's spring game, with all three quarterbacks throwing touchdown passes.
Born in Mississippi with family ties to New Orleans, Brennan waited until he was a fourth-year junior to get his chance to start in 2020, taking over for Joe Burrow, who had won the Heisman Trophy and led the Tigers to a national championship the season before.
In three starts, Brennan threw 11 touchdowns and three interceptions. But he suffered a torn muscle that ended his season early.
The following year, he broke his left arm in a fishing accident.
Max Johnson, who started for LSU last season, transferred to Texas A&M in December.
LSU opens the season against Florida State on Sept. 4 in New Orleans.