Under NBA rules, the contract cannot be finalized until Thursday.
The 6-foot-7 Roberson averaged a career-best 6.6 points and 5.1 rebounds last season for the Thunder, but he has emerged as a valuable defender during his four years in the league.
Joining Roberson and the Thunder next season will be forwards Paul George and Patrick Patterson. Oklahoma City landed George in a trade last month and signed Patterson as ownership attempts to build around star guard Russell Westbrook.
Roberson, drafted No. 26 overall in 2013, also averaged 5.1 rebounds, 1.2 steals and 1.0 blocked shots in 79 regular-season games this past season.