The 28-year-old was due to be out of contract this summer, but his new deal will see him remain at the City Ground until the end of next season.
Cohen's time at Forest has been hampered by injury and he recently made his return after 16 months out injured.
"It's been a crazy journey," Cohen, who first joined Forest in 2007, told the club website. "We've come so close to the Premier League a couple of times and I've had to come back from injuries. The amount of support I've had from the club, the chairman especially, has made me desperate to stay.
"As I'm sure the club will agree, these negotiations were very easy. I came on my own to one meeting with a realistic idea of what I wanted. I've been very injury prone over the years so the terms of the deal are more based on me playing football, which is only right.
"It's not a sympathy year from the club. The chairman and manager see me as being a part of the team, which is important for me. I'm here to play games."
Left-sider Cohen has not started a league game since September 2014, but he did start Forest's two FA Cup games in January.