Bledsoe became the fourth Kentucky player taken in the draft after the Wildcats spent most of last season as the No. 1-ranked team in the nation.
The 6-foot-1 freshman set a school record with eight 3-pointers while scoring a career-high 29 points in Kentucky's win against East Tennessee State in the NCAA tournament.
Bledsoe joins a backcourt that features Russell Westbrook, Thabo Sefolosha and last year's first-round pick, James Harden.
The Thunder are coming off a season with a 27-win improvement that ended with a loss to the Los Angeles Lakers in the first round of the playoffs.