Bryant announced his decision Tuesday night via Twitter, posting a video of game highlights and workouts, along with him reading the poem "The Test of a Man," about overcoming adversity, with the hashtag #ShowMe.
Bryant will have a chance to step in immediately for the Tigers, who say goodbye to four-year starter Drew Lock.
Bryant was 16-2 as a starter for Clemson, including leading the Tigers to the College Football Playoff in 2017 and starting the first four games of this season.
The arrival of highly regarded freshman Trevor Lawrence created a QB battle for the Tigers last spring, however, and Clemson coach Dabo Swinney said from the outset of the season that Bryant would be fighting to retain his job.
After being a critical part of the Tigers' win over Texas A&M in Week 2, Bryant saw his reps decline. After a Week 4 win over Georgia Tech in which Lawrence was particularly sharp, Swinney announced a change.
"Kelly took us to the Sugar Bowl and to the Playoff and 12 wins," Swinney said about the QB battle. "But when we came in the spring, and Trevor was here in January, you have to earn it every year. So we had a quarterback competition. And I was very up front with that in the spring. They competed all the way. And Kelly came out of camp ahead, but it was close enough to where we said, look, we're going to play them right out of the gate. We're going to play both guys, and we're going to see if it settles on the field."
Bryant skipped practice the following Monday but told Swinney he'd be back that Tuesday. Instead, he announced that Wednesday that he would transfer, suggesting that he hadn't been treated fairly by the Clemson staff.
For the season, Bryant completed 67 percent of his throws with two passing touchdowns and two more rushing.
Bryant's decision was enabled by a new rule that allows a player to participate in any four games of a season without penalty, effectively making 2018 his redshirt year and extending his eligibility through 2019.
After announcing his intent to transfer, Bryant visited a number of schools, including North Carolina, Arkansas, Mississippi State and Auburn before ultimately settling on Missouri.
In parts of four seasons at Clemson, Bryant completed 66 percent of his passes, throwing for 3,338 yards, 16 touchdowns and 10 interceptions. He also rushed for 973 yards and 15 touchdowns.