The deal was reached last weekend and announced by the team on Monday.
Richards went 13-4 with a 2.61 ERA last season and made $520,000. His season ended when he tore the patellar tendon in his left knee while covering first base Aug. 20 in Boston.
He had asked for $3.8 million in arbitration and had been offered $2.4 million offered by the club.
Newly acquired outfielder Matt Joyce is the Angels' only player remaining in arbitration. He asked for a raise from $3.7 million to $5.2 million, and the Angels offered $4.2 million. Los Angeles hasn't gone to an arbitration hearing since 2011.