The clubs announced the deal Monday night.
The 6-foot-10 Slegers mostly pitched in long relief for the American League champion Rays last season, going at least two innings in nine of his 11 appearances while compiling a 3.46 ERA. He allowed just five earned runs over 24 innings in his final 10 appearances, and kept up the strong work with a 1.80 ERA covering five innings in three playoff outings.
Slegers, born in Long Beach, California, has a solid chance to earn an important job in the Angels' bullpen, which is undergoing a major overhaul by new general manager Perry Minasian. Los Angeles had the fifth-worst ERA in the majors last season and missed the playoffs for the sixth straight year.
Mike Mayers, Ty Buttrey and Félix Peña were the Angels' three most-used relievers last season, and they're all still with the club. The next eight busiest relievers from the 2020 roster are gone, and Minasian has traded for closer Raisel Iglesias and signed left-hander Alex Claudio.
Slegers was waived or designated for assignment by Minnesota, Pittsburgh and Tampa Bay in 2019, but he re-signed with the Rays and pitched his way back into the majors last August.
The Angels designated left-hander Dillon Peters for assignment to make room for Slegers.