Yes, except during the hot summer months when he may live at Castel Gandolfo just outside Rome.
Because there is a special church there called St. Peter's Basilica. He also has to live there because he is the leader of the Catholic Church.
The pope lives in the Papal Apartments in Vatican City.
He normally lives in the Papal Apartments in the Apostolic Palace. During the heat of the summer he usually spends that season at Castel Gandolfo just outside of Rome.
Florence, Republic of Florence, Italy and Grand Duchy of Tuscany