Bynum didn't play a single minute for the Philadelphia 76ers last season because of knee injuries was considering a two-year offer from the Cavs.
His contract will include $6 million of the $12 million guaranteed in the first year and a team option of $12 million for 2014-'15.
Bynum, 25, had arthroscopic surgery on both knees in March.
SI.com STAFF: 2013 NBA free agency tracker He will be reunited with Cleveland coach Mike Brown, who has returned to the team after being fired three years ago. Brown and Bynum spent one season together with the Los Angeles Lakers and Bynum had his best season averaging 18.7 points and 11.8 rebounds a game.