Hudson, who emerged as a solid starter in 2006, suffered a right shoulder strain in Spring Training last year. He made only one start for the Royals and went just two innings on May 10 against the Athletics.
Hudson returned to the disabled list and underwent right shoulder surgery on June 28. He's expected to be ready for this year's camp, which opens officially for pitchers on Feb. 14.
A right-hander who previously pitched for the Reds, Hudson has a 17-18 record and a 5.11 ERA in 58 Major League games, including 41 starts.
The Royals still have seven players eligible for salary arbitration.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.