The former Birmingham and Aston Villa boss will begin work tomorrow and will take charge of Saturday's npower Championship encounter with Crystal Palace at the City Ground.
"I'm delighted to welcome Alex to our club and look forward to working with him," Forest chairman Fawaz Al Hasawi said on club website nottinghamforest.co.uk. "Alex took Birmingham to promotion from the Championship and has great experience of working in the Premier League."
He added: "He's hungry for more success and I believe he's the man who can help us fulfil our ambition of making it to the Premier League."
The 53-year-old McLeish, who has also had spells in charge of Rangers and the Scotland national team, had been out of work since being dismissed by Villa in May, after finishing just two points above the relegation zone in the Premier League.
The Scot, who will be presented to the media following training tomorrow morning, welcomed the opportunity to return to management at a club lying eighth in the second tier.
"I'm really looking forward to working with Nottingham Forest," McLeish told Forest's website.
"I've had time away from the game and now feel refreshed and ready to go.
"The fact that a club of Forest's magnitude has offered me a job excites me greatly - it's a wonderful opportunity.
"I can't wait to get started and I'm looking forward to meeting the players, talking to them and taking my first training session."
- Sports & Recreation