"We all need to give Brian Hoyer a chance," O'Brien said. "... I believe in him. I believe in his ability to run our offense efficiently."
Hoyer competed with Ryan Mallett for the starting job throughout the Texans' voluntary and mandatory offseason programs and through the first two weeks of training camp. Both players signed two-year deals with the Texans in the offseason, with Hoyer's deal worth $10.5 million and Mallett's worth $7 million.
The quarterbacks were told of the decision together in a meeting Monday morning.
"A sense of excitement, a sense of accomplishment ... and realizing that it's just the beginning," Hoyer said. "My being named the starter today doesn't mean that anything is going to be given to me. I have to go out and earn it every day. It's an honor and privilege to be able to do that. From here on out I have to go out and prove to my teammates, prove to everyone in this organization that I can be a winning starting quarterback for this team."
The 29-year-old Hoyer started Houston's preseason opener earlier this month against San Francisco, throwing a touchdown pass to Cecil Shorts III on the team's opening drive. Hoyer took the rest of the game off while Mallett played the remainder of the first half and second-year QB Tom Savage played the second half.
Mallett started Saturday's game against Denver. Neither Hoyer nor Mallett was able to get the Texans into the end zone against the Broncos.
"I think at this point there's definitely things that need to be corrected and get fixed," Hoyer said after the game, "but I don't feel poorly about where I'm at. I don't know if I'd say I feel great. I think we have a long way to go as an entire offensive unit, myself included."
O'Brien has often stressed that what happens in games and on the practice field was only part of the team's evaluation of its quarterbacks.
Hoyer and Mallett both have served as backups to Patriots quarterback Tom Brady and were teammates in New England for one year after the Patriots drafted Mallett in 2011. When Hoyer signed with the Patriots as an undrafted free agent in 2009, O'Brien was the team's quarterbacks coach.
"When he came to New England as an undrafted guy out of Michigan State, he was a wide-eyed guy," O'Brien said of Hoyer. "He settled down pretty quickly. He made that team, he beat out a couple guys who had been there for a while, and there he backed up Tom, and for a long time we only kept two quarterbacks. ... He did a good job in that situation. From that point to where we are now ... his life has changed."
Hoyer started 13 games last season for Cleveland before eventually losing the job to rookie Johnny Manziel. The Browns started 7-4 with Hoyer under center, but the seventh-year veteran struggled down the stretch, throwing seven interceptions over a three-game stretch.
He appeared in 14 games last season, passing for 3,326 yards, 12 touchdowns and 13 interceptions. The Ohio native sparked Cleveland to a three-game winning streak in 2013 before suffering a season-ending knee injury in Week 5.
Mallett, 27, started two games last season, his first in Houston, before suffering a pectoral injury and missing the rest of the year.
The Associated Press contributed to this report.