The Indians announced the signing Saturday, six days ahead of the team's first full-squad workout.
The 42-year-old Giambi spent the past three-plus seasons filling a part-time role with the Rockies. The 2000 AL MVP was a mentor to younger players and he interviewed for Colorado's managerial position this offseason.
Giambi could become the Indians' DH, a role filled by veterans Jim Thome and Travis Hafner in recent years.
A five-time All-Star, Giambi has 429 homers - just one in 89 at-bats for Colorado last year - 1405 RBIs and a .280 average in 18 big league seasons with Oakland, the Yankees and Rockies. Known for his patience at the plate, Giambi has a career on-base percentage of .403.