Matsuzaka, limited to just 18 starts in the past two seasons because of elbow issues, signed a minor-league contract on Wednesday.
Matsuzaka will compete to win a spot in Cleveland's rotation. If he's added to the 40-man roster, Matsuzaka will make $1.5 million this season. He can earn an additional $2.5 million in performance bonuses.
Matsuzaka went 50-37 in six seasons with the Red Sox, who signed him to a $52 million contract in 2007. He went a combined 33-15 in his first two seasons, but is only 17-22 since 2008. He underwent reconstructive elbow surgery in 2011.