The deal comes with $4 million in possible incentives, according to Olney.
Anderson started eight games for the Colorado Rockies in 2014, going 1-3 with a 2.91 ERA and 1.315 WHIP. He had season-ending back surgery in August and the Rockies later declined a $12 million option on him for 2015.
The 26-year-old spent the first five years of his career with the Oakland Athletics, going 26-29 with a 3.73 ERA and 357 strikeouts in 450.1 innings. Anderson is a former second-round draft pick by the Arizona Diamondbacks in 2006.
In 2011, Anderson underwent Tommy John surgery and made only six starts the following season.
The Dodgers went 94-68 last season, winning the NL West. They lost to the St. Louis Cardinals in four games in the NLDS.
- Molly Geary