The 50 year old has signed a three year contract and will meet the media for the first time as Forest manager on Thursday.
Chief Executive Mark Arthur said: "The club moved quickly to secure his services as it is rare for a manager and coach of his undoubted calibre to be available.
"Steve has a proven track record of coaching and managing at club level, having played a key role in helping Manchester United secure the Champions League trophy, three Premier League titles and an FA Cup; guided Middlesbrough to the League Cup and also to the final of the UEFA Cup and led FC Twente to their first ever Dutch title.
"We are delighted to have him on board at The City Ground."
