McLeish has installed Peter Grant as deputy manager, while Jimmy Floyd Hasselbaink has been allowed to leave his role as first-team coach.
Grant, who managed Norwich between 2006 and 2007, had coaching roles at Celtic, West Ham and West Brom before assisting McLeish at Birmingham and then Aston Villa.
"He's a workhorse and his life is soaked in football," McLeish, speaking to Forest's official website, said of his new number two. "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."
Former Chelsea striker Hasselbaink joined the coaching staff at Forest in July 2011, while he worked towards his UEFA 'A' Licence.