The Swiss were renowned for their skill in battle and valued highly as a military unit in multiple armies and multiple periods of history, ranging from the times of Tacitus, who had said: "The Helvetians are a people of warriors, famous for the valour of their soldiers." to (and beyond) the 1500s, where the Pontifical Guard were established. One of the major reasons why they became the protectors of the Holy See (They are listed in the Annuario Pontificio under "Holy See", not under "State of Vatican City" - The Gendarmerie is the Vatican City), aside from their proficiency, is also how, and largely due to a single person. (Despite the fact that many popes had hired them previous to the permanent guard being formed)

During the time of the Borgias, and the Italian Wars, the swiss were once again hired by the various participants, amongst which was Cardinal Giuliano della Rovere, the future Pope Julius II (1503–1513), who was well acquainted with the Swiss having been Bishop of Lausanne years earlier. Because of his experiences with them, in 1503 he asked the Swiss to provide him with a constant corps of 200 Swiss mercenaries. In September 1505, the first contingent of 150 soldiers started their march towards Rome, under the command of Kaspar von Silenen, and entered the city on 22 January 1506, today given as the official date of the Guard's foundation. "The Swiss see the sad situation of the Church of God, Mother of Christianity, and realize how grave and dangerous it is that any tyrant, avid for wealth, can assault with impunity, the common Mother of Christianity," declared Huldrych Zwingli, a Swiss Catholic. Pope Julius II later granted them the title "Defenders of the Church's freedom" due to their previous actions in shaping Italy during the afore mentioned wars (Which are rather interesting, and would easily fill up a thread on its own).

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I mainly used the Vatican website as my source, which goes into far greater depth than I, so be sure to check it out here.