The versatile 26-year-old, the club's current player of the year, skippered the Reds on several occasions during the 2012/13 campaign in the absence of Danny Collins.
He was thrilled to accept manager Billy Davies' offer, telling Forest's official website: "It's a massive honour to be captain of such a huge club.
"I'm really looking forward to it but nothing is going to change with me. I just want to set examples in the way I play football, which is something I have always tried to do."
Midfielder Andy Reid has been named vice-captain, a move Cohen has welcomed.
He added: "The manager knows how much experience Reidy has. He has been at some massive clubs and is used to big pressure situations, which will come into play in the coming months.
"He and the other experienced players in the team will be crucial to us this season."