Downes makes the step up with immediate effect having worked as part of Forest's scouting network for several years.
He told the club's official website: "I am delighted to be joining the club on a full-time basis and look forward to the challenge ahead."
Downes made more than 500 appearances during a playing career that included spells at Peterborough, Rochdale, Watford, Barnsley and Blackpool, where he also coached.
He has also been on the coaching staff at Aston Villa, Port Vale, Wolves - where he also had a spell as caretaker manager - Watford and Blackburn.
Forest chairman Fawaz Al-Hasawi added: "Bobby brings a wealth of experience to the role and we are very pleased to have him on board in such an important position."