The Angels reached the deal with Parker on Thursday.
The 32-year-old Parker's deal also includes award bonuses. He gets a raise from $560,000 last season.
Parker was largely outstanding during 71 appearances in his first season with the Angels. He had a 2.54 ERA over 67 1/3 innings, going 3-3 with eight saves.
Parker also has pitched for the Cubs, Yankees and Mariners. The Angels claimed him off waivers from the Brewers in December 2016, and he lived in an RV with his wife and stepson after making the Halos' roster last spring.
Los Angeles has eight other arbitration-eligible players.