The Angels made their signing of free-agent reliever Joe Smith official on Wednesday, after the right-hander passed a physical. The three-year deal, first reported on Saturday, is worth $15.75 million.

To clear space for Smith on their full 40-man roster, the Angels designated right-hander Juan Gutierrez for assignment.

Smith, who will turn 30 in March, comes to the Angels after five productive seasons with the Indians. He made at least 70 appearances for Cleveland in each of the past three years, with a 2.42 ERA, a 1.16 WHIP and a 2.2-to-1 strikeout-to-walk ratio.

The sidearmer should help bolster the back end of the Angels' bullpen, which also includes closer Ernesto Frieri and lefty Sean Burnett. The club's relievers finished 26th in the Majors last season with a 4.12 ERA.

Gutierrez began last season with the Royals, but the Angels claimed him off waivers in July. The 30-year-old made 28 relief appearances for Los Angeles, posting a 5.19 ERA across 26 innings, striking out 28 and walking 12. The five-year veteran also has pitched for the Astros and D-backs.