George had surgery for a partially torn tendon in his right shoulder and his status will be evaluated before the start of the 2019-20 season.
George also will have surgery on a small labrum tear in his left shoulder in the coming weeks, the team said in a statement.
Westbrook had two procedures. One was for a torn ligament in a finger on his left hand. The other was an elective arthroscopic procedure on his right knee. He is expected to return to basketball activities in approximately three weeks.
Westbrook averaged a triple-double for the third straight season with 22.9 points, 11.1 rebounds and 10.7 assists per game.
Both players had their procedures in Los Angeles.
ESPN was the first to report the surgeries.
George ranked second in the league with 28 points per game this season, and he led the league with 2.21 steals per game. Both shoulders hampered him in the final two months of the season.
Before that, he was considered among the leading candidates for the league MVP award and the Thunder were one of the top teams in the Western Conference.
With both stars banged up, the Thunder faltered late in the season and lost to Portland in five games in the first round of the playoffs.
"I just was frustrated," George said after the Thunder were eliminated late last month. "I think it came at a terrible time, especially the team was rolling. We were playing good. I was holding up pretty, pretty, pretty good. I just thought it came at the wrong time, honestly. But again, I’ve never made no excuses on it. I was dealing with it for a long time throughout the season. It just got worse and worse as it went on."
George mostly played through the pain. His shoulders were heavily taped and he often had a heating pad on his right shoulder when he wasn’t on the court.
"Injuries are part of the game," George said. "I’ve missed a season being hurt, so I was able to — the training staff assured me I was fine to play through it, and I will be fine going forward. I’d had no other thought in my mind but to be out there and play and ride it out with my guys."