Mordecai, who backed up Kyler Murray, Jalen Hurts and Spencer Rattler at OU, beat out highly touted freshman Preston Stone, a four-star recruit who was ranked No. 121 in the ESPN 300 and chose SMU over LSU, Penn State, Texas and USC.
Oklahoma coach Lincoln Riley praised Mordecai in December when the quarterback announced he was entering the transfer portal.
"I think he's been a really good member of this football team," Riley said. "I think he's ready to be a starter. He's had some good competition while he was here. He had some unfortunate events that made it tougher for him to compete, like getting injured during our competition this year. But he's a great young man, a tremendous quarterback and he'll make somebody very happy."
Riley's brother, Garrett Riley, is SMU's quarterbacks coach and co-offensive coordinator.
Mordecai, a 6-foot-3, 218-pound junior from Waco, Texas, completed 50 of 70 passes for 639 yards with four touchdowns and one interception in 12 appearances at Oklahoma.
At SMU, he replaces Shane Buechele, who transferred from Texas and threw for 7,024 yards and 57 touchdowns in two seasons as SMU's starter.
The Dallas Morning News first reported that Mordecai had won the Mustangs' starting quarterback job.