Giambi, 42, will attempt to fill the role of designated hitter for the Indians. He's spent the past three and a half seasons working as a power bat off the bench for the Colorado Rockies.
Over his 18 years in the majors, Giambi established himself as one of the best power hitters in the game, slugging 429 home runs and driving in 1405 runs. He won the American League MVP award with the Oakland Athletics in 2000 and earned a trio of All-Star selections with the New York Yankees.
He brings a .403 career on base percentage and a reputation for patience at the plate to the Indians.
Matsuzaka, commonly known as Dice-K, posted a 1-8 record and 8.28 earned run average in 11 starts with the Boston Red Sox in 2012, the year after he had successful Tommy John surgery.
He hasn't been an effective pitcher since he went 18-3 with a 2.90 ERA and a fourth-place finish in the AL Cy Young voting in 2008.
He will compete for the fourth spot in the Indians' starting rotation behind Justin Masterson, Ubaldo Jimenez and Brett Myers. He is reunited with Terry Francona, who is the current Indians manager and managed Dice-K in Boston.
The Indians have also signed Myers, Nick Swisher, Mark Reynolds and Drew Stubbs this offseason.