ESPN's Ramona Shelburne reported Wednesday that Morris was picking between the Thunder, Lakers, Rockets and Raptors, among a few other interested teams.
The Athletic first reported the agreement.
Morris, 29, recently was traded by the Wizards to the Pelicans, and then was waived by New Orleans. He last played on Dec. 26 after suffering a neck injury. He recently was cleared to play after receiving a second opinion.
With financial constraints playing a part because of a significant luxury tax bill pending, the Thunder didn't make a deal at the trade deadline, instead hoping to make an addition in the buyout market. Morris will provide versatility to the Thunder's bench, backing up starting power forward Jerami Grant and providing another floor-spacing big in addition to Patrick Patterson.
A 6-foot-10 forward, Morris is averaging 11.5 points, 5.1 rebounds and 1.8 assists in 34 games this season (15 starts).