The Longhorns' announcement came a few hours after the school said it had fired former head coach Tom Herman, who posted a 32-18 record in four seasons at Texas. Under Herman, the Longhorns went 7-3 this year and beat Colorado in the Valero Alamo Bowl on Tuesday.
Sarkisian, who won this year's Broyles Award as the top assistant coach in the Football Bowl Subdivision, said he will remain with the No. 1 Crimson Tide through the College Football Playoff national title game.
The 46-year-old Sarkisian added that he already held a team meeting and met with the current coaching staff at Texas.
"This is a unique and compelling opportunity to lead this storied program to the next level, competing once again amongst the best in college football," Sarkisian said in a statement.
Sarkisian is the first assistant coach hired by Texas to lead its football program since 1951, when the school promoted Ed Price to the position.
In his previous head-coaching stints, Sarkisian posted a 46-35 combined record at USC and Washington. He also served as offensive coordinator of the NFL's Atlanta Falcons in 2017 and 2018 before returning to Alabama in 2019.