The person, who spoke on the condition of anonymity Friday night because the Lions and Browns were not commenting on the trade, said Detroit acquired cornerback Leigh Bodden and a third-round pick from Cleveland after the deal with Cincinnati fell through.
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.
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.