Reyes had his contract selected by the Angels on Friday.
The Angels have three players who are unvaccinated and can't travel into Canada for this weekend's three-game set in Toronto, including two relievers, and Reyes will join the team as bullpen depth. The right-hander last pitched in the majors in 2019 and has a 3.92 ERA, 1.49 WHIP and 52:28 K:BB in 38 appearances with Triple-A Salt Lake this year.