The Dodgers traded two minor-leaguers for League: 22-year-old Class A outfielder Leon Landry, their third-round draft pick in 2010, and Double-A closer Logan Bawcom, taken in the 17th round in 2010.
League was 0-5 with a 3.63 ERA with nine saves for Seattle this season and was demoted from the closer role in late May. He will likely pitch in the late innings out of the bullpen for the Dodgers.
"I've seen this cat in the American League, and he's dirty," manager Don Mattingly said. "He may have had troubles with lefties this year, but he's like (Dodgers reliever Ronald Belisario). When he gets the ball down he gets everybody out. He's filthy. This is a good arm."
General manager Ned Colletti said, "We've watched (League) a lot. He's throwing 95-96 miles per hour with a good split and good slider."