Thompson, who threw for 64 yards and a touchdown last season, will transfer to Utah, and because he will be graduating in May, Thompson will be eligible to play for the Utes in the 2014 season.
Thompson will have two years of eligibility remaining.
Thompson decided to transfer after Trevor Knight emerged as the favorite to start for the Sooners in 2014 after his MVP performance in the Sugar Bowl.
Thompson, the son of former Oklahoma quarterback Charles Thompson, suffered a fractured foot prior to the 2013 season and finishes his OU career with 64 passing yards, one touchdown and one interception in two games played.
Last year's starter Travis Wilson, who missed the final three games after suffering a concussion, will return to the field and participate in spring practice.
Thompson will compete with Wilson, Adam Schulz and Connor Manning for the starting quarterback job.