Perez will earn $2.3 million in his new contract, according to the source. With incentives, he has a chance to earn about $6 million total. If he ascends to the closer role, that could increase to about $8 million, the source said.
Perez, 28, was not tendered a contract by the Cleveland Indians in October after struggling with a 4.33 ERA in 56 games and being arrested in June for having marijuana shipped to his home under his dog's name. He pleaded no contest to those charges and was put on probation, according to reports.
Perez gives the Dodgers four pitchers with experience as closers and plenty of bullpen facial hair. Kenley Jansen will be the closer, and the team signed Brian Wilson for $10 million earlier this month to be his setup man.
The Dodgers also have Brandon League, who was signed to a three-year, $22.5 million deal to close last winter before struggling.
Perez had a career-high 39 saves in 2012, converting all but four of his chances. He missed a month early this past season with a sore right shoulder and was replaced as the Indians' closer late in the season.
Financial terms of the deal aren't known. Perez he made $7.3 million last season. The Los Angeles Times was the first to report that the sides were nearing an agreement.
Perez was in Lake Buena Vista, Fla., earlier this month at baseball's winter meetings to meet with club officials. He spoke with the New York Mets and had drawn interest from the Baltimore Orioles, according to reports.
The Dodgers also announced they have signed long reliever Jamey Wright to a one-year deal. He was with the club in 2012.
ESPN.com senior writer Jerry Crasnick contributed to this report.