The moves were expected as the Knicks continue to overhaul their roster under Donnie Walsh, the team's president of basketball operations, and new coach Mike D'Antoni. Green, a guard, and guard-forward Jones were acquired Monday for forward Renaldo Balkman, a 2010 second-round draft pick and cash.
Balkman became expendable when the Knicks drafted forward Danilo Gallinari with the No. 6 selection in the June draft.
The contracts for Green and Jones aren't guaranteed after Aug. 1.