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The 35-year-old Madson posted a 2.13 ERA in 68 appearances for the Royals in 2015 after missing the previous three seasons because of various arm injuries.
Before the extended time away from the game, Madson was a dominant reliever for the Phillies, saving a career-high 32 games in 2011. He has a 3.45 ERA and 55 saves in 559 Major League games with the Phillies and Royals.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.