The 6-foot-4, 340-pound seven-year veteran fell out of favor in Detroit last season because of his weight and the Lions traded him to Cleveland last Friday.
"I don't think (the weight) will be an issue here," he said.
The deal was completed Wednesday after it fell apart over the weekend when the teams could not reach an agreement on other parts to be included.
Cleveland has decided to send cornerback Leigh Bodden and a third-round pick in the 2008 draft to Detroit in exchange for Rogers, a two-time Pro Bowl selection.
Rogers, 28, has compiled 447 tackles and 29 1/2 sacks since Detroit made him a second-round draft pick in 2001 out of the University of Texas.
Last season, he played in all 16 games and scored the first touchdown of his career on a 66-yard interception return against Denver while recording 66 tackles and a career-high seven sacks.