The deal was announced on Tuesday. The Thunder have a year to use the trade exception.
Thabeet, a 7-foot-3 defensive specialist from Tanzania, played in 66 games in 2012 and averaged nearly a block per contest. His playing time was reduced last season when first-round pick Steven Adams emerged as the backup centre.
The Grizzlies made Thabeet the second overall pick in the 2009 draft. The former Connecticut star also has played for the Houston Rockets and the Portland Trail Blazers.