Multiple reports on Tuesday said the deal would feature an option for a third year.
Putz, an eight-year veteran, spent his first six seasons with the Seattle Mariners and was named an All-Star in 2007 -- his best year in the majors.
Putz appeared in 60 games in 2010 and closed out the season with a 7-5 record while recording three saves and a 2.83 ERA, serving primarily as a setup man for the White Sox.
Putz is 30-24 with 106 saves for his career.
Putz was the third reliever the Diamondbacks acquired on Monday, having traded power-hitting third baseman Mark Reynolds to the Baltimore Orioles for right-handed relievers David Hernandez and Kam Mickolio.
Arizona is looking to rebuild a bullpen that contributed to the Diamondbacks' second straight last-place finish in the NL West.