The 6-foot-4 Thornton averaged 17.2 points per game in his four college seasons, capped by a 20-point average last season. Boston took him with the 45th overall pick.
The Celtics went into the draft hoping to trade for a better pick. But president of basketball operations Danny Ainge said the price was too high.
In the first round, the Celtics drafted guards Terry Rozier of Louisville with the 16th pick and R.J. Hunter of Georgia State with the 28th. With the third pick in the second round, the 33rd overall, they chose forward Jordan Mickey of Louisiana State.