The 5-foot-10, 240-pound Rolle, a sixth-round pick by the Eagles in 2011, had 53 tackles, a sack and a forced fumble in his rookie season, appearing in all 16 games.
He had just four tackles this season after losing his starting job at weakside linebacker to Akeem Jordan in training camp, and had struggled on special teams.
Jordan missed the Eagles' Sunday night victory over the Giants with a hamstring injury but Jamar Chaney was given the start over Rolle.
"Words can't explain the hollow feeling I have right now. Love this city but I'm on to another journey," Rolle, 23, tweeted Tuesday morning.
Newspapers in Philadelphia are reporting that the move was likely as a result of the Eagles' poor kickoff coverage against the Giants, who averaged 36.2 yards on six returns in Sunday night's game.
The 6-foot-2, 230-pound Moten played in 12 games last season for the Colts and Seahawks.