The 53-year-old Scot had been out of work since being dismissed by Aston Villa in May, after finishing just two points above the relegation zone in the Barclays Premier League, but insists he is raring to go at the City Ground.
The former Birmingham City, Rangers and Scotland manager will be presented to the media at a press conference this morning.
Fawaz Al Hasawi, the Forest chairman, last night said: "I'm delighted to welcome Alex to our club and look forward to working with him. Alex took Birmingham to promotion from the Championship and has great experience of working in the Premier League. 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."
McLeish, who will be in the dug-out for tomorrow's home game with Crystal Palace, said: "I'm really looking forward to working with Nottingham Forest. 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."
Forest are currently in eighth spot in the npower Championship.