Born in Pisa, Galli started his career with his home town's youth side as a midfielder before switching to the role of goalkeeper. He began his professional career with ACF Fiorentina in 1977, where he played for nine Serie A seasons. In 1986–87, he joined fellow league side A.C. Milan, being first-choice for three of his four years, and establishing himself as one of Italy's best goalkeepers, winning the Serie A title and the Supercoppa Italiana during his first season. He also started in both of the club's back-to-back European Cup conquests, in 1989 and 1990, also winning consecutive European Supercups in 1989 and 1990, and the Intercontinental Cups in 1989. He also reached the final of the 1989–90 Coppa Italia with Milan. In his final season with the club, he was often alternated and faced competition for a starting spot from back-up Andrea Pazzagli, whom manager Arrigo Sacchi often fielded during league games, while Galli played in European matches.