The loosehead prop played under Edinburgh head coach Lynn Howells during their time together at Leonessa.
The 40-year-old made 69 appearances for his country and previously played for Natal Sharks, Harlequins and Calvisano.
Cuttitta said: "I am happy to be here working with Lynn again and having the opportunity to work with talented players in a professional environment.
"Getting the scrum right is not a quick fix, but I hope I can play my part in solving any problems and forming a solid scrum."
Howells added: "Massimo brings a fresh new approach and ideas to scrummaging which are not the same as most coaches.
"Hopefully, over time, the scrum will give us the platform we require to play an expansive game."