The deal was completed on Tuesday and the Wolves immediately waived Vaden to clear a roster spot to bring in free agent point guard J.J. Barea.
Hayward was a first-round pick last year out of Marquette. He averaged 3.8 points and 1.7 rebounds in 42 games for the Timberwolves, getting minimal playing time on a very young team.
Thunder GM Sam Presti says he likes Hayward's toughness, size and shooting capability and thinks Hayward can provide some depth in Oklahoma City.
Now the Wolves can add Barea, who agreed to leave the NBA champion Dallas Mavericks for a four-year deal with Minnesota on Monday.