The Diamondbacks announced the move Wednesday.
The 36-year-old right-hander was 1-2 with a 3.16 ERA in 24 relief appearances with Seattle last year. Sweeney signed a minor league contract with Seattle last April and opened the season with Triple-A Tacoma.
He has spent parts of four seasons in the majors with the Mariners and San Diego Padres. Sweeney has a career record of 4-2 with two saves and a 3.38 ERA in 117 innings pitched.