Bridwell, 27, was 10-3 with a 3.64 ERA in 20 starts and one relief appearance for the Angels in 2017, then missed much of this year because of right elbow inflammation. He was 1-0 with a 17.55 ERA in one start and four relief appearances over 6 2/3 innings for the Angels and 1-1 with an 8.68 ERA at Triple-A Salt Lake.
Bridwell is 11-3 with a 4.60 ERA for Baltimore and the Angels in 28 games over three seasons. He was designated for assignment last week by the Angels.
The 26-year-old Torreyes was among the most popular players in the Yankees clubhouse, a 5-foot-8 backup often hoisted into the air by teammates to high-five 6-foot-7 Aaron Judge. Torreyes hit .292 with 36 RBI in 315 at-bats over 108 games in 2017, but spent much of this year at Triple-A Scranton/Wilkes-Barre and batted .280 with seven RBI in 100 at-bats over 41 games for the Yankees.
New York announced the moves on Monday.