On Tuesday, Okur joined teammates Carlos Boozer and Kyle Korver, who also had the option of skipping the final year of their contracts and becoming free agents.
None of the three chose to test the market, keeping the Jazz lineup intact for a hefty price.
Okur is due $9 million next season. He has averaged 16 points and eight rebounds since joining the Jazz five years ago and is the team's top 3-point shooter.
The Jazz struggled without him when he missed the first three games of the playoffs this spring with a hamstring injury, falling behind the Los Angeles Lakers and never recovering.
"He has clearly been an integral part of our success since his arrival and we are hopeful that he will continue to perform at such a high level in the future," O'Connor said.