Boss Steve Cotterill moved for the 20-year-old left-back after Clint Hill was recalled from his loan spell by QPR.
The 20 year old has made five substitute appearances, while he also had a spell on loan with Leicester last season.
Cotterill told Forest's official website: "Left-backs are very difficult to come by and although he's only a young player I think he's got a good future ahead of him.
"They have a big squad of players at City which allowed him to go out on loan and we're delighted to have him.
"We had a vacancy at left-back and Greg is the perfect fit for us."