"We think, after what he did, closer is the role," Colletti said. "That's what he was in Seattle in 2011 and part of 2012. We acquired him and the last few weeks, obviously he was very, very solid. So that's where we start."
Colletti said he considers this winter's crop of free-agent closers "relatively thin" with demand relatively high.
"You look at that and it's always better to get somebody you know, even for a short time," he said. "We had him in the clubhouse, saw how he prepares. And the coaching staff plays a vital role in the players you go after and retain. That's why we made this a priority."
Combined with his time in Seattle, League was 2-6 with a 3.13 ERA and 15 saves in 21 opportunities, appearing in 74 games. He finished the season with scoreless relief in 20 of his last 21 appearances, allowing one run and eight hits over 22 1/3 innings.
"It's official! Couldn't be more proud and happy to call LA my home for the next 3 years!" League tweeted. "Looking forward to seeing everyone this spring. Thank you to Ned Colletti, the entire @Dodgers organization, and fans for this opportunity!"
League is a seven-year veteran and was an All-Star for the Mariners in 2011, when he had 37 saves. He earned $5 million this year, but lost his closer's job in Seattle with erratic outings, which led to his trade.
Working with pitching coaches Rick Honeycutt and Ken Howell, League resolved a mechanical flaw that helped him rediscover the nasty splitter that made him tough to hit.
"Everybody goes through ups and downs, struggles, but it's not the end of the world," said Colletti. "We saw him up in Seattle while he was going through it. He has a lot of ability. He got here, it took a little while to get acclimated. But Kenny Howell and Rick Honeycutt did a great job changing his delivery a little bit, and at the end of the season he was as good as anybody in baseball."
Colletti earlier said that re-signing League was one of the club's top offseason priorities, especially with the uncertain health of Jansen, who underwent a surgical procedure last week that the club believes will cure the irregular heartbeat.
Colletti said he tried to acquire League from Seattle last winter because of his "power stuff, great split." He spoke with League before the season ended to establish the interest was mutual and had several conversations and a meeting with League's agent that led to the deal.
Jansen now figures to share setup duties with Ronald Belisario and be League's backup at closer. Colletti said he's still looking to add another reliever.
Colletti said he also has had conversations about free-agent left-handed reliever Randy Choate (who shares League's agent) and remains interested in re-signing Jamey Wright, but no talks have been held. Already under contract or control for 2013 are relievers Matt Guerrier, Scott Elbert, Javy Guerra, Shawn Tolleson, Paco Rodriguez and Josh Wall.
Despite the large number of relievers, Jansen is coming off heart surgery, Elbert had elbow surgery, Guerra finished the year with a strained obligue, Guerrier missed most of the season with elbow problems but avoided surgery and Belisario has a history of substance-abuse and visa issues.
Colletti, responding to an Internet report that the Dodgers were open to trading outfielder Andre Ethier, said: "It hasn't been discussed."