Street, who turns 31 on Aug. 2, is a two-time All-Star, including this year. He had a 1.09 ERA in 33 appearances for San Diego this season, with 24 saves in 25 opportunities.
A 10-year veteran of the A's, Rockies and Padres, Street is 35-27 with a 2.87 ERA and 258 saves in 300 chances in his career.
The Angeles, who have been going with Joe Smith as their closer, acquired former Pirates closer Jason Grilli in a trade late last month.
Bowden misidentified one of the players going to the Padres from the Angels. They are: Second baseman Taylor Lindsey, shortstop Jose Rondon and right-hander R.J. Alvarez (not Jose).
- Chris Mascaro