The TL;DR version of it would be: depending on whom you ask, either because it was by far the most prestigious literary language among the vernaculars of Italy, or for that very same reason plus the fact that in the XVI century Tuscans were over-represented in politics and business.

But it must be emphasized that things could well have been different. The process of standardizing (written) Italian began in the XVI century, and the proposal that eventually won was championed by Venetian scholar Pietro Bembo (1470-1547). He proposed to adopt a literary language closely modeled on XIV century Florentine-language authors Boccaccio (prose) and Petrarca (poetry), to which somewhat reluctantly he added Dante (his style struck him as obscure and unpolished, go figure).

Interestingly, his proposal had at least two contestants, both of which at first sight made a lot more sense than his. The first alternative was the “Florentine theory”, championed by political theorist Niccolò Machiavelli (1469-1527), among others: since Florentine was to be the Italian literary language, why not to choose modern (i.e., XVI century) Florentine? It would have felt a lot less artificial, and would have been easier to learn (well, Florentines would have had it much easier, others not so much).

The second alternative was the “courtesan theory”, championed by various scholars, among which Baldassarre Castiglione (1478-1529). They argued that since professionals and officials with different mother dialects already worked together at the courts of Italian lords, literary Italian should have been based on those people’s lingua franca: an artificial language that would not unfairly disadvantage non-Tuscan officials and scholars.

At first, the Bembo party won the hearts of literary authors themselves. The most egregious example is Ludovico Ariosto (1474-1533), from Emilia, who rewrote the 1532 edition of his The Frenzy of Orlando to bring it in line with Bembo’s policy. Orlando being the smashing international hit that it was, this fact alone might have done a lot to help the Bembians win the day.

In any case, by the end of the century the question was fundamentally settled. The Dukes of Savoy adopted classical Florentine/Italian (as opposed to Latin) as official language of the administration in 1560, and other States (Grand duchy of Milan, Tuscany, the Papal States), while not making it a matter of official policy, started doing the same. The use of Italian was also attested at the Neapolitan court. At that point, the only major exception was Venice, who stayed faithful to Venetian for official uses, but whose publishers printed Italian language books at an impressive rate.

Unfortunately, I cannot recommend any work in English on these topics. This one is a concise account by a leading scholar that might survive a Google Translate run:

Claudio Marazzini. 2016. “Questioni linguistiche e politiche per la lingua”. In S. Lubello (ed.), Manuale di linguistica italiana. Berlin: De Gruyter. 633-654.