There was a convergence of a number of factors in the nineteenth century that allowed unification to come to pass in the Italian peninsula under the auspices of Savoyard monarchy.
Firstly, the Napoleonic experience had popularized a notion of national unity. Although Napoleon's reorganization of the Italy was predicated upon subordinating Italian to French interests, it gave the peninsula something approaching a unified administration. Counter-intuitively, both experience within the French administration and resistance to French rule provided a common experience to the charter generation for Italian nationalism. Although the governments of Restoration Italy were decidedly against nationalism and other ideological imports from the French Revolution, the national idea percolated through Italian secret societies and various emigres. Somewhat ironically, while the experience of Napoleonic rule helped foster calls for national unity, Napoleon's administrative system strengthened the Restoration states' ability to react to insurrections. For example, even the arch-reactionary Kingdom of Sardinia kept the Napoleonic system of tax collection and revenue administration. This strengthened state system easily put down revolts in Naples in 1820 and Modena and Parma in 1831.
The result of the Italian states' reactionary attitude was a stalemate between the revolutionary nationalist forces led by the Mazzini/Garibaldi clique and the largely conservative governments of the Italian states. By the mid-nineteenth century both sides were clearly frustrated with this state of affairs. There's a wonderful Italian word, campanilismo (love/loyalty to one's bell tower- i.e. hometown), which encapsulated the frustration of nationalists. Both Mazzini and Garibaldi hoped that their calls for unification would lead to the Italian masses abandoning their princes and joining a republic. There was a brief hope in the widespread revolutions in the peninsula in 1848 that liberal republicanism would triumph, but the actions of the Austrian general Radetzky snuffed out the nascent republics and restored Austrian power in the peninsula. On the state side of the equation, a few adept officials, the foremost among them Cavour, recognized that an alliance with nationalism would benefit and preserve the old order longer than simply reacting against the conspiracies and invasions orchestrated by the nationalists.
The mid-century geopolitical situation allowed for these two camps to merge together despite being at loggerheads since 1815. Austria's successful counterattack against the republics of 1848 led to the restoration of monarchies in central and southern Italy and was a potent reminder that a great power could thwart any attempt to unify the peninsula without the support of a great power. Because of Austria's actions in 1848, the nationalist realized that the Kingdom of Sardinia was their only viable option. The Austrians had helped to restore governments that possessed an hostility to both unification and liberal forms of governance. Of the post-1848 government, only the Kingdom of Sardinia retained the revolutionary constitution of that year.
The French injected a further element into this picture. Louis Napoleon thought he could pose as the champion of the national idea and thus cover the second French empire with glory. Cavour realized that an alliance with the French and the nationalists would strengthen the Kingdom of Piedmont-Sardinia. When Napoleon III realized that Italian unification ran counter to French interests, he reversed course and Cavour's successor, Ricasoli, hitched his star to Prussia.
Neither the nationalists nor the new Italian monarchy was very fond of this arrangement. Victor Emmanuel II was not really prepared to rule as a constitutional monarch but recognized that he would have increased powers as King of Italy rather than just Piedmont-Savoy. The liberal-orientated nationalists stomached an alliance with the monarchy because it was the best route towards a quick and relatively painless unification. Their hope was that after a few generations of parliamentary experience and unification, the new Italian state would create the Italian national identity that they spent fifty years trying to create.
Sources
Beales, Derek Edward Dawson. The Risorgimento and the Unification of Italy. London: Allen and Unwin, 1971.
Mack Smith, Denis. Cavour. New York: Knopf, 1985.
_.Mazzini. New Haven: Yale University Press, 1994.