Padron, 6-foot-4, 233 pounds, set a Mustangs passing record in 2010 with 3,828 yards and 31 touchdowns.
J.J. McDermott took over last season, and former Texas quarterback Garrett Gilbert has transferred to SMU.
"I felt comfortable with being able to pick up the system and how well the system prepares a QB to get to the next level," Padron said. "There is more responsibility the QB has there than what I'm coming from and the guys they have coming back, especially at WR are very intriguing.
"The coaches and their motivation to compete and be the best was the biggest thing for me though, because they want to win a conference/national championship as bad as I do."
Padron was pulled in SMU's 46-14 loss to Texas A&M in the Sept. 4 season-opener after throwing two interceptions in the first four passes. McDermott entered for the third series and played the rest of the game. McDermott led the Mustangs to five straight wins after that.
Former SMU quarterback Bo Levi Mitchell was a two-season standout at Eastern Washingon, an FCS program, which was 6-5 last season.