"The Giants had a great year," League said. "They won the games they needed to win. But I think in 2013, the Los Angeles Dodgers are going to be the team everyone wants to beat or tries to beat."
The 29-year-old closer spoke to reporters on a conference call after he signed a $22.5-million, three-year deal with the Dodgers.
League was a free agent but agreed to terms with the Dodgers before he was eligible to sign with other teams. He said he had no interest in finding out what else was out there.
"I didn't feel the need to test the market because the Dodgers were No. 1 on my list," League said.
League recalled that soon after he was traded to the Dodgers by the Seattle Mariners on July 31, he told his wife and agent that he could see himself playing in Los Angeles for a long time. League, who has three children, makes his off-season home in San Diego.
League said he doesn't care how Manager Don Mattingly uses him, pointing to how teammates Kenley Jansen, Ronald Belisario and Javy Guerra all have experience closing. But League acknowledged feeling an obligation to fill the ninth-inning role, considering he will be earning a closer's wage.
"Absolutely," League said.
League couldn't imagine any of this happening to him early in the 2012 season, when he lost his job as the Mariners' closer.
"You can't make this stuff up," League said of how he was traded to the Dodgers, fixed some mechanical problems and finished the season with a 0.40 earned-run average in his last 21 appearances.
"Now we know what to look for, whereas when I was with Seattle, I had no idea what I was looking for," he said. "I was trying to correct problems that weren't even problems."