League's salary will reflect his role, as the Dodgers are committed to paying him $22.5 million over the next three seasons. The contract also includes an option for a fourth season at $7.5 million that will become guaranteed if League finishes 55 games in 2015.
"We think that after what he did the last two or three weeks, that closing is the role," General Manager Ned Colletti said.
League, 29, was acquired for two minor league players from the Seattle Mariners at the July 31 nonwaiver trade deadline and finished the season as the Dodgers' closer. He posted a 2.30 earned-run average in 28 appearances and converted all six of his save opportunities. His ERA was 0.40 over his last 21 appearances.
His end-of-the-season form was considerably better than at the start of the season in Seattle, when he was displaced as the Mariners' closer. League was an All-Star closer with the Mariners in 2011, when he saved 37 games.
With League closing, Kenley Jansen figures to be a set-up man next season. Jansen, who closed for most of the season, is recovering from heart surgery.
In League, Jansen and Ronald Belisario, the Dodgers have three power arms to pitch the seventh, eighth and ninth innings. Colletti said he is still looking to make additions to a bullpen that posted a 3.23 ERA this year, fourth-best in the National League.
The Dodgers felt an urgency to sign League as soon as possible because of a lack of alternatives on the free-agent market. The only healthy closers who figure to be available this off-season are Rafael Soriano and Jose Valverde, who had a nightmare of a postseason with the Detroit Tigers.
"It's just my opinion, but it's not a robust market," Colletti said. "It's not like you have eight, 10 choices."
Colletti's top priority will now be to find a No. 2 or No. 3 starting pitcher to complement ace Clayton Kershaw. Colletti said his desire to add a starting pitcher hasn't been affected by news that Chad Billingsley is expected to pitch next season. Billingsley faced the possibility of off-season reconstructive elbow surgery, which would have sidelined him for all of 2013.
Kershaw lost the title of best defensive pitcher in the NL to Mark Buehrle of the Miami Marlins, who won the American League award last year with the Chicago White Sox. Ethier was a finalist in right field and Gonzalez at first base in the American League, where he played for most of the season with the Boston Red Sox. Ethier and Gonzalez were beaten out by Jason Heyward of the Atlanta Braves and Mark Teixeira of the New York Yankees, respectively.
More shocking was that Mike Trout of the Angels didn't win a Gold Glove, as Adam Jones of the Baltimore Orioles was awarded the center field prize in the AL.
A leading candidate for AL rookie of the year and most valuable player, Trout led all major league outfielders by robbing hitters of four home runs, including a June 27 catch at Baltimore's Camden Yards in which he raced to the fence and leapt several feet over the wall to pull back a J.J. Hardy drive.
Trout also stole home runs from Gordon Beckham in Chicago on Aug. 4 and Seattle's Miguel Olivo in Anaheim on Aug. 11, and ended a Sept. 8 home game against Detroit by robbing Prince Fielder of a home run.
Times staff writer Mike DiGiovanna contributed to this report.