The Royals acquired Santana along with cash from the Angels in exchange for minor-league hurler Brandon Sisk, the teams said.
Santana, 29, was dealt just after Los Angeles exercised its $13 million option for his services in 2013.
The right-hander was once one of the rising stars of the Angels staff but is coming off a tough 2012 season in which he went 9-13 with a 5.16 ERA over 30 starts overall. He picked it up a bit at the end of the season, however, going 4-3 with a 3.63 ERA over the final two months.
Santana is probably best known for a July 27, 2011, no-hitter for the Angels against the Cleveland Indians.
Sisk went 3-2 with eight saves in 50 games last season for Class AAA Omaha this past season.