League was 0-5 with a 3.63 ERA in 46 games this season for the Mariners. He lost the closer job in late May after blowing four of his 13 save opportunities.
"I've seen this cat in the American League, and he's dirty. He may have had troubles with lefties this year, but he's like (Ronald Belisario)," manager Don Mattingly said. "When he gets the ball down he gets everybody out. He's filthy. This is a good arm."
General manager Ned Colletti said League throws 95-96 miles per hour with a sinker and a slider. League will likely pitch in the later innings, as a setup man to Kenley Jansen.
"Any time you can add people in that segment of the game, that's a good spot to have," Colletti said.
The trade for League appears to have opened the door for the Dodgers to deal another reliever, Josh Lindblom, in a deal for Shane Victorino of the Phillies, as has been widely reported as a close deal.
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