The former Carlisle United man ends his three-year stay at the City Ground during which time he made 55 appearances and scored 10 goals.
Garner was signed as a 20-year-old by the Reds for a £1m+ fee.
"I just can't wait to get out there," he told the Forest website at the time.
"The stadium and the pitch look superb and everything I have seen of the Forest set-up looks top drawer.
"I've known about the transfer for several weeks and was very excited about the prospect of coming here.
"It's a fantastic move for me at this stage of my career and I am looking forward to getting out there and helping Forest try to get into the Premier League."