Weber, the Gophers' all-time passing yards leader, has started 38 consecutive games for Minnesota but had to compete this spring to retain his job after struggling in 2009.
"We thoroughly evaluated every aspect of quarterback play throughout the spring and Adam has earned the right to be the starter entering the 2010 season," Brewster said on gophersports.com. "MarQueis Gray will be our No. 2 quarterback, with Moses Alipate No. 3.
"In the final analysis, Adam's command of the offense, his leadership, decision-making and his overall play won out."
Weber earned second-team All-Big Ten honors in 2008 but struggled last fall, completing just 52 percent of his passes and throwing two more interceptions (15) than touchdowns (13). Minnesota ranked last in the Big Ten in both scoring (20.9 ppg) and total offense (306.5 ypg) last season.
Brewster said before the team's appearance in the Insight Bowl that the quarterback job would be up for grabs this spring. Gray was Weber's primary challenger.
Weber will work with his third offensive coordinator in as many seasons as Jeff Horton takes over the play-calling duties for 2010. Horton has tried to simplify the scheme, and both Weber and Gray welcomed the change.
Weber told ESPN.com in April that he began taking most of the reps with the first-team offense several days into spring practice.
"It's my job to lose," Weber said. "That's how I look at it. Every day I go out there, if I don't perform at the standards I believe I should play at, it's tough. I still get very frustrated. But that's the great thing about competition. You never get calm. You never sit back on your heels.
"I always have to be full go, because if I don't perform, they're putting another quarterback in and I might never see the field again, so it's a great motivator."
Adam Rittenberg covers Big Ten football for ESPN.com. He can be reached at firstname.lastname@example.org.