It will be the first time he has managed in England since his spell in charge of the national team ended in humiliation with the country failing to qualify for Euro 2008.
He signed a three-year deal at Forest, who came close to promotion to the Premier League this season but lost in the playoff semi-finals. He succeeds Billy Davies, who was sacked on Sunday.
"The club moved quickly to secure his services as it is rare for a manager and coach of his undoubted calibre to be available," Forest Chief Executive Mark Arthur said in a statement on the club website.
The 50-year-old McClaren has been keen to repair his tarnished reputation in England after his ill-fated spell in charge of the national team, when he was dubbed "The Wally with the Brolly" after putting up a big umbrella to shield himself from the rain during a match.
"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," Arthur said.
"We are delighted to have him on board at the City ground."
