In the trade, the Padres will receive triple-A second baseman Taylor Lindsey, double-A reliever R.J. Alvarez, whose fastball sits in the 97-mph range, and Class-A shortstop Jose Rondon, who played in Monday night's All-Star Futures Game.
The Angels are expected to officially announce the trade after Friday's game against the Seattle Mariners.
Street, 30, is 1-0 with a 1.09 earned-run average in 33 games for the Padres this season. He has converted 24 of 25 save opportunities, limited opponents to a .158 average, struck out 34, walked seven and allowed only 18 hits for an 0.76 WHIP (walks plus hits per inning).
His fastball isn't overpowering — it usually sits in the 90-mph range — but it has good sinking action and is effectively mixed with a slider and changeup.
Street, a 10-year veteran and two-time All-Star who also has pitched for Oakland (2005-2008) and Colorado (2010-2011), is in the final year of a five-year, $36-million contract that pays him $7 million this season and includes a very reasonable $7-million team option for 2015.