Percival, 35, earned $7.5 million last season. The Angels will replace him with Francisco Rodriguez, 22, who earned $375,000 last season and is expected to make between $400,000 and $500,000 next season.
Percival, a four-time All-Star, earned the save in Game 7 of the 2002 World Series, as the Angels won their lone championship in their 44-year history.
On Friday, the Angels decided not to retain third baseman Troy Glaus, the most valuable player of the 2002 Series, and handed the position to rookie slugger Dallas McPherson.
Percival posted 33 saves last season and a 2.90 earned-run average, including a 1.69 ERA after sitting out three weeks in June because of a strained right forearm. Rodriguez, an All-Star last season, posted a 1.82 ERA.