Sources told The Athletic and MLB Network that the team signed the free agent to a one-year, $9 million contract. Incentives can push the deal to $10.5 million.
The Angels have yet to announce the transaction, which is pending a physical.
Cahill, 30, was 7-4 last season with a 3.76 ERA in 21 appearances. He started 20 games for the Oakland Athletics during his 2018 campaign. The 10-year veteran signed with the Athletics last offseason in free agency. He posted a 4.93 ERA and a 4-3 record in 21 games for the San Diego Padres and Kansas City Royals in 2017.
Cahill owns a career 4.08 ERA and an 80-83 record in 304 career appearances.
The Angels added the right-hander to their rotation just two days after signing fellow right-hander Matt Harvey on a one-year, $11 million pact.