The Angels are paying Street $7 million this season. The new deal extends through 2017, with a club option for 2018.
Street, 31, is tied for second in the American League with 11 saves this season. He is 2-1 with a 3.29 earned-run average.
Street has made the All-Star team in two of the previous three years. His 91.9% conversion rate on save opportunities over the last five years leads the majors among pitchers with at least 50 opportunities.
The Angels acquired Street and minor league pitcher Trevor Gott last July from the San Diego Padres for four minor leaguers.