The short answer is that a new “Signoria,” or executive committee, was constituted: formerly composed of representatives of the city’s trade guilds (susceptible to corruption by bankers like the Medici) the new council was instead composed of eight notables appointed with an unclear selection process, while all tax-paying citizens over the age of 29 elected an eighty-man body that while tempting to classify as a legislature, was more akin to a regulatory or supervisory council (separation of powers was not a well-developed concept in Italian political thought at the time).

But the friar Savonarola had no true institutional role. He had certainly been enormously influential: his sermons had been an important catalyst turning the public mood against the Medici and pushing the citizenry to take action against them. His preaching would continue influence the public mood in Florence until late 1497, that is to say until the very end of his tenure as de facto head of government. Indeed, Savonarola would actively advise the Signoria, act as a representative for the Florentine Government in foreign affairs, and could also count on support from most of the Tuscan clergy in not only augmenting the public’s vitriol against the now-banished Medici, but also in pacifying the Florentine Republic to his rule.

However, Savonarola’s influence on Florentine society was never total. Although the Medici had been banished, their supporters continued to exert economic and social influence in the city’s affairs. This pro-Medici faction would colorfully come to be called the “Gli Arrabbiati,” meaning “The Angry,” in political discussions. When King Charles of France, whose war on the Kingdom of Naples had caused the panic and crisis which led to Savonarola's ascension, would be chased from Italy by a military coalition composed of all the Italian States except for Florence, "Gli Arrabbiati" were quick to pounce on this legitimizing turn of events. Savonarola’s preaching about the imminent apocalypse had proven less than accurate, and King Charles turned out not to be the antichrist Savonarola's most arduous followers had interpreted! As the public’s fervor died down, Papal excommunication would further delegitimize him, and once the Medici’s supporters regained political control of the government Savonarola would be arrested and gruesomely executed.

But this question has further implications that might be surprising. I’m almost certain of why you’re asking it: Savonarola’s ascension is normally treated in a single paragraph by generalist histories of Early Modern Europe. The ouster of the Medici cryptogovornment in favor of the inflammatory clergyman Girolamo Savonarola is regarded as a symptom and signal that the prosperity of the Italian Renaissance is over, and the balance of power in Western Europe has definitively shifted to the larger polities across the Alps. This is a point that is difficult to debate. While readers might be left scratching their heads at how this precisely could come to pass, there might not be much value for the generalist to look into the details of how the reactionary Savonarola came to govern one of the most important governments in 15th century Italy once the general forces at play have been expoused. However, an Italianist might argue that Savonarola’s rise is demonstrative of the defining features of the Italian political system that would keep the peninsula divided until the 19th century, influencing the fluctuating but always perceptible Italian contribution to the social narrative of Europe and mitigating Italy’s role in European affairs thereafter.

In the early 1490s, the high officers of the Italian polities were in a state of deep panic and disarray that far outmatched the periodic crises that had previously afflicted the peninsula’s political order. The traditional histories would blame this disarray on the scheming of the ruler of Milan, Ludovico Sforza, called “The Moor” (“Il Moro” in Italian). While we will see later that there were clear structural forces rendering Italy susceptible to foreign invasion, attributing the end of the Renaissance and start of the Italian Wars on Il Moro is nonetheless tempting: Ludovico's regency for his hedonistic nephew, the Duke of Milan Gian Galeazzo Maria Sforza, was characterized by wanton cruelty, paranoia, and ruthlessness. Gian Galeazzo’s marriage to Isabel of Aragon, a granddaughter of the King of Naples, had been machinated by the late Duke Galeazzo Maria Sforza (Ludovico’s older brother). The plan had been to guarantee lasting peace and stability on the Italian peninsula. However, Ludovico was not a man conditioned to trust in peace. His rise to the regency had largely been a consequence of his resilience to betrayal: His brother’s work to persuade the King Louis XI of France that Milan was the leading state in Italy would instead convince the King to order his murder; his brother’s consort, Duchess Bona of Savoy, then expelled the late Duke’s brothers from Lombardy and occupied Milan with men-at-arms loyal to her own brother, the Duke of Savoy; only after a hard-fought struggle claiming the life of all the Sforza brothers save Ludovico would “The Moor” be granted a place in the regency council, a position from which he would eventually imprison Bona of Savoy in the castle of Abbiategrasso, execute her trusted councilors, and govern the duchy on his own. His regency, lasting well into his nephew’s twenties, focused on preservation of the Milanese state and its ruling dynasty.

As Ludovico organized a lavish wedding for his teenage nephew, he must have already felt misgivings about the young man’s ability to defend the polity which his brothers had given their lives to preserve. But while Gian Galeazzo’s disinterest in the government of his state might have reinforced this sentiment, his new bride had a markedly different idea. Rapidly grasping what was happening, the new duchess Isabel would attempt every possible political scheme to undercut Ludovico, eventually leading to the Moor’s decision to betray his alliance to the King of Naples. Ludovico would support the new King of France Charles VIII in usurping the Kingdom of Naples, a bold and fatal decision that would ultimately unleash a series of political crises in Italy while also demonstrating to the whole continent that the peninsula was a ripe ground for occupation, exploitation, and conquest. This is the sort of climate in which the figure of Savonarola would emerge.

Further elaboration and conclusions continue below.