The 37-year-old Brennan died at 12:03 a.m. at Hoag Memorial Hospital Presbyterian, Newport Beach, according to Orange County coroner records.
Brennan's death was due to a drug overdose, but "at this time there is no investigation from our department," Costa Mesa police spokeswoman Roxi Fyad told NBC News. Fyad did not reveal what drug was involved in the overdose.
"Rest in aloha, Colt," his alma mater said in social media posts.
Brennan, a Southern California native, was a three-year starter for Hawaii, throwing for 14,193 yards in 38 career games. That's the second most in school history, trailing only Timmy Chang's 17,072 in 53 games.
Brennan took the Warriors to heights not seen again since his time at the school. In his final year on campus in 2007, Hawaii recorded the school's only undefeated regular season, going 12-1 with their only loss to perennial superpower Georgia in the Sugar Bowl.
Brennan finished third in Heisman Trophy balloting that year, behind winner Tim Tebow of Florida and Arkansas star Darren McFadden, and ahead of Missouri's Chase Daniel.
Brennan was a passenger in a serious 2010 car accident in Hawaii.