The Cavs announced the move Saturday, one day after LeBron James said he's returning to Cleveland.
A 12-year veteran, Haywood has played in 794 NBA games, averaging 6.9 points and 6.1 rebounds. He missed all of last season with a broken foot.
The 7-footer gives Cleveland some front line depth, but he's also only got one year left on his contract. Haywood, who played on Dallas' 2011 title team, was picked by Cleveland with the 20th overall pick in 2001 but traded on draft night to Orlando.
Powell played four years at Stanford, averaging 10.8 points and 6.3 rebounds. The 6-11, 240-pound forward is the fourth Canadian on Cleveland's roster, joining Tristan Thompson, Anthony Bennett and Andrew Wiggins, this year's top overall pick.