League is 0-5 with a 3.63 ERA and nine saves in 46 games for the Mariners this season, but he's only one year removed from being an All-Star after converting 37 saves in 2011. The Dodgers gave up outfielder Leon Landry and pitcher Logan Bawcom in the deal, and Colletti said he thinks both have the ability to one day make the Majors.
"He's a veteran that has closed games before," Colletti said. "He has pitched at the end of games. He can help us anywhere from the seventh, eighth, ninth inning."
The 29-year-old reliever has a 2.70 ERA in his last 18 appearances, and Colletti isn't concerned about his struggles this year. League was involved in the no-hitter thrown against the Dodgers earlier this season.
Colletti added the Dodgers were interested in League this time last season and again during the winter, but the Mariners weren't willing to make a deal.
"We've watched him a lot," said Colletti, who orchestrated a trade for Hanley Ramirez and Randy Choate earlier this week.
Manager Don Mattingly was excited about the deal following Monday's 7-2 loss to the D-backs. He said he's not sure where League will fit into the bullpen with the team using Kenley Jansen and Ronald Belisario as its closer and setup man. However, he said League is the sort of pitcher opposing hitters don't want to see late in games.
"I've seen this cat in the American League, and he's dirty," Mattingly said. "He may be having trouble with lefties this year, but this guy is like [Belisario]. When he's getting the ball down, he's getting everybody out."
Mattingly went on to say he is familiar with League, and added the reliever is a good arm that is capable of throwing 96-97 mph. He pitched for Toronto from 2004-09 before joining the Mariners in 2010. He has a career record of 17-27 with a 3.69 ERA, 54 saves and 282 strikeouts in 349 games.
The Dodgers will announce a roster move to make room for League on Tuesday.
Colletti said he was done making moves for the night after pulling off Monday's trade. But with time still on the clock before Tuesday's Deadline, he didn't rule out another trade happening.
"Hopefully," Colletti said about the potential for a last-minute deal.
Alex Angert is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.