Knight, who was elected as a team captain by his teammates for a second straight season, will be Mayfield's backup. Thomas will be No. 3 on the depth chart.
"It's been a very tight battle among those three guys," coach Bob Stoops said in a statement. "Baker, Trevor and Cody have all made substantial progress, and I feel we can win with any of them."
Mayfield will lead the Sooners' new up-tempo, spread scheme implemented by first-year offensive coordinator Lincoln Riley.
Coaches have raved about Mayfield's leadership style, as teammates have gravitated toward his confident, outgoing demeanor. Earlier this summer, Stoops said Baker is "an excellent leader, is highly competitive and has a good delivery."
The 6-foot-1, 209-pound Mayfield was the Big 12 offensive freshman of the year with the Red Raiders in 2013, when he passed for 2,315 yards with 12 touchdowns and nine interceptions.
He sat out last season after Texas Tech declined to give him a release to transfer within the Big 12, even though he was never on scholarship at the school.
ESPN Staff Writer Jake Trotter contributed to this report.