Calhoun, who lives in Tempe, hit 33 homers for Angels in 2019.
Arizona introduced pitcher at Chase Field on Tuesday.
Right-hander had 3.55 ERA in 71 games with Milwaukee in 2019.
He hit .207 with nine homers for Arizona this year.
Outfielder Steven Souza Jr., pitcher Taijuan Walker and catcher Caleb Joseph are all granted free agency.
The latest from Star columnist Greg Hansen.
Arizona's 40-man roster now has a full 40 players.
The Star's Greg Hansen writes about Arizona's uneven exhibition win, why the Wildcats' women's golf team is poised for big things and the late…
Dave Martinez was tossed in the seventh inning of Tuesday's Game 6.
Arizona won a surprising 85 games to finish second in NL West.
Arizona ends season with five straight wins and 85-77 record.
Arizona wraps up season with games Saturday and Sunday against San Diego.
Goldy gets loud ovation in first game back in Phoenix after playing for Arizona from 2011-18.
Arizona is six games out of wild card race with six games left.
Padres fall in Rod Barajas' debut as manager.
Arizona remains 5.5 games behind Milwaukee for second wild card with nine days left in season.
Miguel Rojas drives in six in Marlins' 12-6 victory Tuesday night in Phoenix.
Arizona remains 5.5 games out of second wild card with 13 days left in regular season.
Arizona 5.5 games out of wild card after losing 3-1 to visiting Cincinnati on Sunday.
Arizona is 4.5 games behind Cubs for second wild card.