The Bengals had been looking to move the former USC standout after re-signing Manny Lawson last week.
Rivers was picked ninth overall by Cincinnati in the 2008 NFL Draft. He started 13 games for the Bengals in 2010, when he recorded 77 tackles and one sack. Rivers missed the entire 2011 season with a wrist injury.
The trade leaves the Bengals with Lawson, Rey Maualuga and Thomas Howard as likely starters this season. The team also could re-sign free agent Brandon Johnson.
In New York, Rivers will join a linebacker corps that includes Michael Boley, Greg Jones and Mathias Kiwanuka.
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