Grant worked alongside the Scot at Birmingham before following McLeish to Aston Villa in summer 2011.
The former Norwich boss also has experience as assistant to Alan Pardew at West Ham, and McLeish is delighted to have Grant on board.
He said: "He's a workhorse and his life is soaked in football. He's also had massive experience of English football, having worked here for many years.
"I've known him for a long time and he's a person I trust and respect enormously. I am sure he will do an excellent job for Nottingham Forest Football Club."
Meanwhile, Jimmy Floyd Hasselbaink has left the club after 18 months at the City Ground.
He was first appointed as part of Steve McClaren's non-playing staff in July 2011.