Grassi, who is a product of the Parma youth system, told RedWeb: "I have enjoyed my time here on trial and I'm happy I impressed the manager enough to win a deal.
"I can't wait to play my first match in front of the home crowd and hopefully I will get my chance against Motherwell on Saturday."
Dons director of football Willie Miller believes the defender arrives at Pittodrie with a fantastic pedigree.
"We're delighted to have Davide on board for the season ahead," said Miller.
"He's a player who has come through the youth ranks at Parma so he has a good basis from which to develop.
"He's a tall and powerful left-sided defender and I know the manager has been impressed by what he's seen of him so far."