"I'm absolutely delighted that Chris has signed," said Royals boss Brian McDermott after his club paid a fee believed to be over £2m for the 22-year-old Welsh international full-back.
"He was very, very keen to come to us and is another player who is young and very hungry.
"He's already played more than 200 games at club level, plus another 37 for his country, which is phenomenal for someone so young."
Gunter leaves behind a club still without a manager after Mick McCarthy ruled himself out of the running to succeed Steve Cotterill after talks with Forest's new owners.
Glenn Hoddle is now the clear favourite with the bookmakers but Peterborough are expecting an approach for Darren Ferguson and Roy Keane's representative has hinted that the Irishman would be keen on the job.