Street spent the past 3 1/2 seasons of his 13-year career with the Angels, who held a $10 million club option for 2018. Instead, the two-time All-Star gets a $1 million buyout.
Street appeared in just four games last season due to injury.
The 34-year-old reliever had knee surgery after his career-worst 2016 season ended early. He missed the first 2 1/2 months of 2017 with a strained lat muscle before missing even more time with a groin injury and a mild rotator cuff strain.
Nolasco led the Angels with 181 innings as the only durable starter in their injury-plagued rotation, but went 6-15 with a 4.92 ERA in his 12th big league season. The Angels paid him a $1 million buyout.
Los Angeles also sent Guerra outright to Triple-A Salt Lake. Several hours later, the 28-year-old veteran chose free agency instead.