Cotterill has signed a three-and-a-half-year deal at the City Ground after a compensation package was agreed with former club Portsmouth.
"I'm very excited - it's a wonderful football club which has great traditions which should be embraced," he told Forest's official website.
"I'm really looking forward to getting to work on the training pitch with the players.
"I like to think of myself as hard working, honest and a winner."
The 47-year-old will officially take charge on Monday, so he will not be in the dugout for tomorrow's clash at Coventry City. Assistant Rob Kelly will manage the side for the match at the Ricoh Arena.