Wilson, 32, joined the Dodgers for the final two months of the 2013 season after recovering from a second Tommy John surgery, and he was lights out through the postseason.
Wilson received a contract that paid $10 million in 2014 with a player option worth $10 million for '15 that he exercised after the '14 season. If he is signed by another club, the Dodgers will be responsible for all of the salary except for $507,500, the Major League minimum.
Wilson tried to pitch through arm discomfort this Spring Training, went on the disabled list in April and never regained his velocity or command. He was unable to reliably handle the setup role while his ERA soared to 4.66 and his fastball rarely hit 90 mph.
Wilson is one of the 20 players inherited by new club president of baseball operations Andrew Friedman that is no longer with the team.
Club general manager Farhan Zaidi said earlier this week that the move on Wilson was not because there was anything wrong with his arm, but management was convinced that Wilson no longer was "one of the best seven reliever options."
During the winter, the club has acquired relievers Chris Hatcher, Joel Peralta and Juan Nicasio.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.