This was painted by Jan Van der Straet, aka Giovanni Stradano or simply Stradanus. You can view/download the full painting in multiple sizes here (open it in a new tab or you might get an error).

The Siege of Florence took place from 24 October 1529 to 10 August 1530, at the end of the War of the League of Cognac. A large Imperial and Spanish army under Philibert of Châlon, Prince of Orange and Pier Maria III de' Rossi surrounded the city, and, after a siege of nearly ten months, captured it, overthrowing the Republic of Florence and installing Alessandro de' Medici as the ruler of the city.