"I've always believed in Myles," Orgeron said.
Brennan will succeed Joe Burrow, the NFL's 2020 No. 1 pick who led the Tigers to a national title and won the Heisman Trophy last season.
The junior quarterback has made 17 career appearances, 10 of which came last season during LSU's near-weekly blowout wins. Brennan completed 24 of 40 pass attempts for 353 yards with a touchdown in 2019.
"The only thing we don't know - and we do believe he'll do very well - is how he'll do under fire," said Orgeron.
The sideline boss added that Brennan might have better arm strength than Burrow, and he lauded his new starter's accuracy.
The reigning national champions will be defending their title without 19 starters from last year's team, including top receiver Ja'Marr Chase.