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.
After being sacked by England in 2007 he took up a post at Twente Enschede and steered the club to their maiden Dutch title in 2010.
Last year he became the first English coach at the helm of a Bundesliga club when he took over at VfL Wolfsburg but lasted just nine months in the job as the 2009 German champions became involved in the battle to avoid relegation.
He was sacked in February.
Before his stint as England boss he had been viewed as a promising manager having worked as an assistant to Alex Ferguson at Manchester United in 1999-2001 before being appointed manager at Middlesbrough, with whom he won the 2004 League Cup.
He also took Middlesbrough to the 2006 UEFA Cup final, where they lost to Sevilla, and Forest will be hoping McClaren can have a similar impact at the club as they seek a return to the top flight.
"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."
