The Thunder reportedly beat out several other suitors, including the Houston Rockets, Brooklyn Nets, and Toronto Raptors.
The Washington Wizards dealt Morris to the New Orleans Pelicans in a cash-cutting move ahead of the trade deadline. He was subsequently released.
The 6-foot-10 forward hasn't appeared in a game since Dec. 26 due to a neck injury, but he was recently cleared to resume basketball activities.
The 29-year-old Morris averaged 11.5 points and 5.1 rebounds in 34 appearances with the Wizards this season.