Brennan steps in for Joe Burrow, who threw 60 touchdown passes in 2019 and had perhaps the best season in college football history. Burrow, a former transfer, won the Heisman Trophy and led the Tigers to the national championship before being selected No. 1 overall in the NFL draft by the Cincinnati Bengals.
A junior from Mississippi, Brennan has appeared in 17 games in his career, including 10 last season.
Coach Ed Orgeron lauded Brennan's accuracy and said his arm strength might be better than Burrow's.
"I've always believed in Myles Brennan," Orgeron said.
He later added: "The only thing we don't know -- and we do believe he'll do very well -- is how he'll do under fire."
LSU heads into the season opener down 19 starters from last year's team, including star wideout Ja'Marr Chase.