The Giants announced the moves Saturday, less than 24 hours before their game in New Orleans against the Saints.
New York made the moves because starting linebacker J.T. Thomas is going to miss the game with an ankle injury and middle linebacker Jon Beason is questionable with an ankle injury.
Morris has been on the practice squad since Sept. 16.
McGee was signed to the practice squad Oct. 14, and to the active roster four days later. He played against Philadelphia on Oct. 19, and was inactive vs. Dallas last week.