The Angels released Abreu on Friday after the 38-year-old journeyman got off to a painfully slow start in limited at-bats.
Because the Angels cut him, the Dodgers would only have to pay Abreu a prorated version of the veteran's minimum.
Abreu had gotten just 24 at-bats in the first three weeks and was batting .208. The Angels thought they had come close to trading Abreu twice, first to the New York Yankees and then to the Cleveland Indians. Abreu grumbled publicly a couple of times about his limited role.
Abreu signed with the Angels before the 2009 season. He appeared in 456 games for them and batted .267 with 43 home runs and 246 RBIs. The two-time All-Star is one of four players all-time with at least 500 doubles, 250 home runs and 350 stolen bases.
The Dodgers have gotten off to a surprising 17-8 start that has them in first place in the NL West. The team's new owners, led by Magic Johnson, officially took hold of the organization Wednesday.
Information from ESPNLosAngeles.com's Mark Saxon contributed to this report.