Financial terms of the deal were not available. He made $7.3 million this year with the Cleveland Indians.
Right-hander Perez, 28, went 5-3 with a 4.33 ERA and 25 saves in 2013 for Cleveland. In the past four seasons as the Indians closer, Perez collected 123 saves.
Perez, who was arrested for marijuana possession in June and put on probation in September after pleading no contest, joins a Dodgers bullpen that includes Brian Wilson, J.P. Howell, Paco Rodriguez, Brandon League, Chris Withrow and closer Kenley Jansen.
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Cincinnati Reds general manager Walt Jocketty said the team will go with speedy prospect Billy Hamilton as the starting center fielder and leadoff hitter for next season.
The Reds lost Choo Shin-soo to the Texas Rangers in free agency last week and their trade proposal to the New York Yankees for Brett Gardner was turned down, leaving Hamilton as the next viable option for Cincinnati.
"He's the guy," Jocketty told the Cincinnati Enquirer. "We feel confident he can be a good leadoff hitter. He'll give us great defense. The only question is how often he can get on base."
Hamilton, 23, batted just .256 at Class AAA last season, but stole 13 bases in 14 attempts for the Reds after a September callup. He set a minor league record with 155 steals in 2012 and swiped 75 this year.
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The Minnesota Twins signed right-handed pitcher Mike Pelfrey and catcher Kurt Suzuki to contracts.
The deals were agreed upon last week. Pelfrey, who pitched last season for Minnesota, signed a two-year, $11 million deal. Suzuki, who played for Washington and Oakland in 2013, signed a one-year, $2.75 million contract.
Minnesota outrighted outfielder Darin Mastroianni to Class AAA Rochester to make room on the 40-man roster.