Ambrosini ended an 18-year spell with AC Milan last summer, joining Fiorentina on a free transfer.
The 36-year-old believes that he still has plenty to prove despite a successful career in Serie A, insisting that Florence provides the perfect platform to do just that.
He told Corriere della Sera: "I'm here because of the project. In football, the project word is often used at random.
"However, the project is for real here, the quality of play, ambitious youngsters, an identity as a team. But patience is needed and the development could cost us something. As was the case in Milan.
"I also chose Fiorentina because I had to prove something to myself. I'm satisfied with how things are going, but let us not get carried away. We are only at the beginning."
Montella's side currently sit sixth in Serie A ahead of a crunch clash this weekend, hosting defending champions Juventus at the Stadio Artemio Franchi.