McClaren's last club job in England was with Middlesbrough, while he has also had spells in charge of Dutch side FC Twente and Wolfsburg in Germany.
"Steve has a proven record of coaching and managing at club level," said Forest chief executive Mark Arthur.
"The club moved quickly to secure his services as it is rare for a manager and coach of his undoubted calibre to become available."
Former England coach McClaren will be officially unveiled by Forest at a news conference on Thursday.
His appointment comes after Davies paid the price for the club's failure in the Championship play-offs for the second season in a row.
Forest football consultant David Pleat believes McClaren's experience of coaching abroad will stand him in good stead.
"The point about Steve McClaren is that he's tested himself," Pleat told BBC Radio 5 live.
STEVE McCLAREN COACHING TIMELINE
1995: Becomes assistant to Jim Smith at Derby after spell as Oxford Utd youth team coach
1999: Moves to Man Utd as number two to Sir Alex Ferguson
February 2001: Joins Sven-Goran Eriksson's coaching set-up with England
June 2001: Appointed as Middlesbrough manager
February 2004: Wins Carling Cup with 2-1 win over Bolton in final
May 2006: Named as Eriksson's successor as England boss
November 2007: Sacked by England after failing to reach Euro 2008
June 2008: Returns to management with FC Twente
May 2010: Wins Dutch title before switching to Bundesliga side Wolfsburg
February 2011: Parts company with Wolfsburg after poor results
June 2011: Appointed as Nottingham Forest boss
"He's come back from a difficult experience with England where had it not been for a goalkeeper mistake [by Paul Robinson in Croatia] and the rain that night [against Croatia at Wembley] which meant having to put up an umbrella, he wouldn't have been ridiculed."
"But he's fought back terrifically well to get a championship [with FC Twente] against PSV and Ajax. He's been doing what he does best - coaching - and we shouldn't underestimate him.
"I think he's done his miles and certainly deserves the opportunity to be at a club that is well run, progressive and will get into the Premier League. How soon? No one knows. They've just missed it for two years running but they're close and I'm sure the club is in good hands."
McClaren's remarkable success with Twente - winning the club's first domestic league title - in the Netherlands helped to rehabilitate a reputation badly undermined by his unsuccessful 16-month spell as England boss.
McClaren, a former Hull, Bristol City and Oxford United midfielder, began his coaching career with Derby before moving on to work under Sir Alex Ferguson at Manchester United.
His success at Old Trafford, including the 1999 Treble-winning season, led to him taking his first managerial position with Middlesbrough in 2001.
McClaren won the Carling Cup in 2004 to earn Boro their first major trophy and also led the Teesiders to the Uefa Cup final in 2006 before replacing Sven-Goran Eriksson as England boss.
The Yorkshireman had recently been linked with vacancies at Aston Villa and Fulham, while Twente - who are in next season's Champions League - were interested in bringing him back to the Netherlands, despite his struggles with Wolfsburg.
"He realises he has to prove his managerial capabilities all over again in England, despite the lure of a more lucrative offer from his former club FC Twente," said BBC Radio 5 live's Midlands football reporter Pat Murphy.
"With Billy Davies leaving behind a talented squad, Forest will be short odds for promotion next May."
Forest were relegated from the top flight in 1999 and have been unable to claw their way back, with their spell in the Football League including three seasons in League One from 2005 to 2008.
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