The move had been expected since Jenks struggled with injuries that affected his performance in the second half of 2010. Jenks, who made $7.5 million last season, was in his last year of being arbitration eligible. He could have received an arbitration award in the neighborhood of $9 million in 2011.
The Sox also exercised the $2.75 million option on Alexei Ramirez, who forced the issue earlier this week when he opted out of his $1.1 million contract for 2011.
Ramirez had no intention of leaving the White Sox, but with his high-level play in recent years he knew he had the leverage to opt out of his 2011 salary to essentially more than double his earnings when the White Sox activated the option.
Ramirez led American League shortstops this past season in batting average (.282), slugging percentage (.431), home runs (18) and total bases (252). He is the first shortstop in White Sox history to win a Silver Slugger Award.
After the 2011 season, Ramirez will be finished with the four-year deal he signed before the 2008 season. But he will remain under the White Sox's control through 2013 as an arbitration-eligible player.
The White Sox also chose Thursday to not give a contract to lefty reliever Erick Threats.
Threats was 0-0 with an 0.00 ERA in 11 games before tearing a ligament in his pitching elbow on Aug. 27.
Doug Padilla covers the White Sox for ESPNChicago.com and ESPN 1000. Information from The Associated Press was used in this report.