In exchange, Cleveland will receive wide receiver Chansi Stuckey, linebacker Jason Trusnik and two draft picks.
Edwards, the third overall pick in the 2005 draft, had been dealing a number of off the field issues; most recently an incident when he punched a friend of Cleveland Cavaliers star forward LeBron James Monday night outside a nightclub.
The fifth-year veteran from Michigan has caught 10 passes for 139 yards this season for the winless Browns. In total, he's compiled 238 catches for 3,697 yards and 28 touchdowns, but has faced criticism in Cleveland last season for the number of passes he dropped.
Edwards' best season came in 2007 when he caught 80 passes for 1,289 yards and 16 touchdowns. His presence in New York should give rookie quarterback Mark Sanchez the target he's been looking for.