General Manager Dennis Lindsey, who joined the Jazz two years ago, will direct the process of finding a new coach.
Lindsey cited "a lot of different criteria over multiple years" for the decision not to retain Corbin. The Jazz tied for the NBA's fourth-worst record (25-57) in 2013-14, while trying to balance the goals of winning and developing young players.
Asked about philosophical conflicts, Lindsey said it would be fair to "assume that there were some different thoughts," but added he was "completely comfortable with the minutes that our young guys got."
Lindsey described Corbin's reaction to the news as ranging "from disappointment to anger and everything in between."
A former Jazz player, Corbin was in his seventh season as an assistant coach when Sloan suddenly resigned.
The team subsequently traded guard Deron Williams in a rebuilding strategy.
The NBA lockout in 2011, having several key players in contract years in 2012-13 and the extreme youth movement of this past season also made Corbin's job more complicated.