The team announced the move Wednesday after Smith took his physical. The sides agreed to terms last weekend on a deal that should boost the Angels' bullpen.
The 29-year-old Smith was 6-2 with a 2.29 ERA and three saves in 70 appearances covering 63 innings this year for Cleveland. He has 13 wins over the past two seasons.
The submarining right-hander spent the past five years with the Indians after pitching for the New York Mets in his first two major league seasons. He is 27-16 with a 2.97 ERA in 439 career games, all in relief.
Smith's contract includes $500,000 annually in potential bonuses.
To make room on the 40-man roster, the Angels designated right-hander Juan Gutierrez for assignment.