Camp is poised to put pen to paper on the deal at Carrow Road after coming through a medical at the club this week.
Norwich have confirmed the deal will be wrapped up subject to relevant paperwork being completed after the Northern Ireland international was told by Forest that he would not be offered fresh terms at the Championship club and was free to move on.
Ahead of his pending move to Carrow Road, Camp told Norwich's official website: "I'm delighted. It all came around pretty quickly and it turned out to be a pretty straight forward decision in the end. I'm really pleased to be here.
"It's a six-month deal which I think suits both parties pretty well. I think it would add a little bit of competition and hopefully I can add to the experience and competition already here. Any player wants to be in the Premier League and I'm very fortunate to be given this opportunity to play at a Premier League club and challenge for a place in the team.
"A few little things have changed around the training ground since my first spell here, but obviously a different atmosphere and feel about the place. I think it was about six years ago now that I was here, how time flies, but it helps to already know the area."
Manager Chris Hughton said: "Lee will give us some really valuable experience alongside Mark Bunn with goalkeeper John Ruddy still out injured for a while.
"He's a proven goalkeeper and he's at a good age. He of course knows Norwich well having had a loan spell here a few years ago and the deal until the end of the season suits all parties.
"He will bring increased competition and will also allow us the chance to search for a loan move for Declan Rudd to get him some good first-team experience somewhere."
Camp previously made three appearances for Norwich while on loan there from Derby in 2006.
He will now look to help Hughton's men preserve their Premier League status this season, with the Canaries having lost five of their last seven league encounters.
Ipswich were also believed to be chasing the 28-year-old but it is East Anglian rivals Norwich who have won the chase for his signature.