The teams announced the deal a day before the deadline to make trades without waivers. Seattle also sent righty reliever Steve Delabar to the Blue Jays for outfielder Eric Thames.
"New league, new hitters, new teammates," League said after the Mariners' 4-1 over Toronto, a game in which he did not pitch. "It's definitely an exciting time. Now, it's a new chapter in my life and go help the Dodgers try and win a ring."
The Dodgers, challenging San Francisco for the NL West lead, sent outfielder Leon Landry and right-handed pitcher Logan Bawcom to the Mariners. Seattle is last in the AL West.
League was 0-5 with nine saves and a 3.63 ERA in 46 games this season. The 29-year-old righty was an All-Star last year when he had 37 saves for the Mariners.
The Dodgers are familiar with League — he got two outs against them in June when six Seattle pitchers combined for a no-hitter against Los Angeles.
League has been particularly tough on right-handed hitters, holding them to a .225 batting average during his career.
League is 17-27 with 54 saves and a 3.69 ERA since 2004 with Toronto and Seattle. He had an inkling a deal might be in the works.
"You can't ignore the rumours and the deadline's the deadline. The past three years you've been hearing stuff whether it be during the trade deadline or even in the off-season," he said.
"But I have said nothing, but expressed how much I love Seattle and wanted to stay here. But, I'm a free agent at the end of the year. You never know what's going to happen ... and this happened," he said.
Mariners general manager Jack Zduriencik said there interest in League.
"A year ago, Brandon had a terrific year. He is walking into a free agent year. At this time, this was probably the wise thing to do for us," he said.
A week ago, the Mariners traded star outfielder Ichiro Suzuki to the New York Yankees. As far as deals, "you have conversations going on and you don't know where it will lead from here," Zduriencik said.
"We'll see. I think that we had worked on these for a while, and this is where we settled," he said.
The 22-year-old Landry went into the day batting .328 with eight home runs, 51 RBIs and 20 stolen bases for Class A Rancho Cucamonga.
The 23-year-old Bawcom had totalled 20 saves and a 2.03 ERA for Double-A Chattanooga and Rancho Cucamonga.