Baker won the Maxwell Award as the national player of the year and the Davey O'Brien Award, which goes to the country's top quarterback, to highlight the College Football Awards Show.
He also was named the Associated Press national player of the year, earning 51 of 56 first-place votes.
Earlier in the day, Mayfield was selected as the Walter Camp Player of the Year by the Walter Camp Football Foundation.
The Big 12 Conference Offensive Player of the Year, Mayfield is the favorite to win the Heisman Trophy on Saturday night.
Mayfield passed for 4,340 yards and 41 touchdowns to lead the Sooners (12-1) to the No. 2 national ranking and into the College Football Playoff. Oklahoma will face No. 3 Georgia in a semifinal matchup at the Rose Bowl.
The 6-foot-1, 220-pound Mayfield beat out a pair of running backs -- Penn State's Saquon Barkley and Stanford's Bryce Love -- to become the third Oklahoma player to claim the Maxwell Award.
Love and Louisville's Lamar Jackson each earned two first-place votes for the AP award. Mayfield, Love and Jackson are the three finalists for the Heisman, which was won last year by Jackson.
Ohio State quarterback J.T. Barrett and Oklahoma State's Mason Rudolph were beaten out by Mayfield for the O'Brien Award.
Houston defensive tackle Ed Oliver won the Outland Trophy emblematic of the nation's best interior lineman. Oliver is the first defensive player to win the honor since current Los Angeles Rams star Aaron Donald in 2013 at Pittsburgh.
The Lou Groza Award for the top kicker went to Utah's Matt Gay, while the Ray Guy Award for the top punter was won by Michael Dickson of Texas.
Scott Frost, who led Central Florida to a perfect 12-0 season that led to his hiring at Nebraska, was named the national coach of the year.