The 23-year-old, currently playing in the Copa America with Argentina for whom he has eight caps and two goals, has signed a five-year deal until June 2026.
Fiorentina reportedly paid 23-million euros ($27.5 million) plus bonuses for the player whose season at Stuttgart was hampered by a muscular injury.
Gonzalez played just once between February and May, having scored six goals in 15 games earlier in the season.
His 14 goals the previous season helped Stuttgart return to the Bundesliga. In total, he scored 23 goals in 79 games for Stuttgart.
Fiorentina are searching for a new coach after former Napoli manager Gennaro Gattuso left three weeks after being appointed following a row over the club's strategy and resources for signing new players.