Anderson's short-term deal with the Grecians has ended and he will now swap Devon for the outskirts of Milan.
City manager Paul Tisdale said: "We are disappointed as a club to see Myles leave, but we're delighted for him as a person that he has been given the opportunity to play football on the continent and experience a new culture and way of life.
"I can't think of many players that have come through the Cat & Fiddle in the past few years that have been more dedicated to improving themselves as Myles. He has developed immensely since joining us in January and he leaves us a better player, both technically and physically.
"It is disappointing to lose a player who ordinarily we would have been keen to tie down on a longer-term deal, but as a club we have to accept our financial situation and the limitations that brings.
"But he has been incredibly dedicated every day during his time with us and he deserves every success in the future. Monza are inheriting a bright and diligent young man and I wish to thank him for all the hard work he has put in."