Thurman, 25, is a graduate of the University of California and arrives at Wolves after a spell in Denmark.
"I'm excited to play for a club that doesn't accept mediocrity, a club where winning is everything," Thurman said.
Thurman comes to Worcester on the recommendation of ex-Wolves forward Will Creekmore, who has left the club.
"I'm delighted to have Robert on the Wolves roster this season, and very much look forward to working with him," said Wolves head coach Paul James.
"He has a tough act to follow in Will, but I'm confident that he will do just that.
"Will brought Robert to my attention, and he should know what it takes to be successful in the BBL after the season he had."
Worcester begin their BBL season with a trip to Newcastle Eagles - the team they beat to win the play-offs - on Friday, 26 September.