Detroit previously was set to get Cincinnati's third- and fifth-round picks, a deal still posted on the Bengals' team Web site late Friday night.
The Lions were aggressively trying to move Rogers, a talented but inconsistent defensive tackle who was due to make a $1 million roster bonus at 12:01 a.m. EST Saturday.
In the deal with Cleveland, they landed a relatively high pick and a player who started for the Browns the past three seasons. The five-year veteran made a career-high six interceptions last season, giving him 11 in a three-year span.
Earlier in the day, the Browns traded their 2008 second-round pick to Green Bay for defensive tackle Corey Williams. Cleveland then signed Williams to a six-year contract that pays him $18 million in guaranteed money and $23 million in the first three years of the deal, according to NFL Network's Adam Schefter.
Williams had been tagged last week as Green Bay's franchise player. He played in all 16 games, including nine starts, in 2007 and set career highs with 51 tackles and 32 solo stops. He tied his career high with seven sacks.
Rogers is among the most dominant defensive players in the league when he is motivated. But he failed to live up to expectations at times because of weight and off-the-field problems.
He was at his best in November, when he lifted Detroit to a rout over Denver and a 6-2 record.
The 6-foot-4, 340-pound Rogers intercepted a pass and rumbled 66 yards for a score, broke up a pass, had four quarterback hits and 2 1/2 sacks, one of which he followed with a somersault. He had plenty of chances to display his signature celebration, gesturing as if he was ripping off his shirt, a la Superman.
"It's just his presence," Detroit coach Rod Marinelli said last season. "I called him the server, because he keeps serving sacks for everybody because he's so disruptive."
But Rogers faded from the spotlight in the second half of the season and the Lions did, too, finishing with only one win in eight games.
He did, however, have a career highs in sacks (seven) and forced fumbles (four) after playing in all 16 games for the fourth time in his seven-year career. He also showed his knack for blocking kicks, making him one of the best in league history. Rogers has blocked 11 kicks, four more than any other player since 1991 -- a decade before his debut.
Whether teams tried to block Rogers with one lineman or two, he often got where he wanted to go with a rare combination of size, speed, strength and nimble footwork.
But he struggled to stay on the field in 2006, getting suspended by the NFL for four games for taking a banned substance to control his weight. He had knee surgery while he was away from the team, didn't play after becoming eligible, then was put on injured reserve with four games left.
Rogers missed just four games over his first five seasons in the league after the Lions drafted him in the second round in 2001, overlooking injury concerns some teams had about him coming out of Texas.
Detroit signed him to a six-year contract in 2005, keeping one of the few players to excel consistently for the struggling franchise.
Copyright 2007 by The Associated Press. All Rights Reserved