Earlier in the day, the Walter Camp Award for best player went to Tagovailoa, while Murray won the Associated Press' Player of the Year.
On Friday, Murray will head to New York City for Heisman Trophy weekend.
Murray was the most exciting player in college football this season and his success has many thinking he could reverse course and choose the NFL over the Major League Baseball. Tagovailoa has thrown for 3,353 yards, 37 touchdowns to four interceptions and has completed almost 68 percent of his passes. Tagovailoa won the Maxwell over fellow finalists Murray and Grier. He's also rushed for 892 yards and 11 scores.
Murray and Tua will also meet at the end of the month in the College Football Playoff.
No. 4-ranked OU, which behind Murray leads the nation in points per game (49.5), yards per game (577.9) and yards per play (8.7; FBS record is 8.6), will make its 52nd bowl appearance when it takes on No. 1 Alabama in the College Football Playoff Semifinal at the Capital One Orange Bowl on December 29 at 7 p.m. CT.
"Kyler Murray has accomplished more in one season and had more impact on the Sooners' tradition in one season than any other player in our history", said legendary former OU coach Barry Switzer. The past four Maxwell winners and past five Walter Camp winners have all gone on to win the Heisman. Mayfield won the award last season. But his left ankle injury and poor performance in the SEC championship game and Murray's great Big 12 championship game performance has made the Oklahoma QB the sportsbook favorite heading into Saturday night.