Grant worked with McLeish at Aston Villa and has now been reunited with the Scotsman after he took the job at the City Ground recently.
"He's a workhorse and his life is soaked in football," McLeish told Forest's official website regarding Grant.
"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."
As a result, former Chelsea striker Jimmy Floyd Hasselbaink has been relieved of his duties as Forest first team coach.