McCoy made five starts last year for Texas and played in 11 games. He threw for 1,045 yards, seven touchdowns and four interceptions.
Ash started six games, while playing in all 13. He threw for 1,068 yards, four touchdowns and eight interceptions. Ash ended the season as the starter.
While both quarterbacks figure to play in the early games, head coach Mack Brown will still need to choose one to go under center for the first snap.
The Texas Longhorns open their season against Wyoming on Sept. 1.