The 35-year-old Shields, who endured two injury-disrupted seasons the last two years of his 10-year career, had a lifetime record of 46-44 with an earned run average of 3.18, and averaged 8.1 strikeouts per nine innings.
"Scot was a huge part of our success over the course of his career here," Angels manager Mike Scioscia said in a statement. "He definitely understood the challenge of pitching late in games and in doing so became the best set-up man in baseball."
Shields, who won a World Series with the Angels in 2002, retires as their all-time leader in relief victories and ranks second in appearances behind Percival.
Since the "hold" statistic for preserving late leads in games was created in 1999, Shields owns the American League record with 155, leading the league in holds for four consecutive seasons from 2005.
(Writing by Larry Fine, Editing by Frank Pingue)