On July 25th 1571 Pope St. Pius V issued a Papal bull recognizing the University – the text of which is available (in Latin) at the University of Salamanca site. Initially providing teaching in theology and the literature, the University later diversified to include faculties of law and medicine by the end of the seventeenth century, and Mathematics and Science during the nineteenth century.
If you wish to learn more about the University (and can read Spanish) see the History of San Marcos page on the University’s web site.
It is worth noting that another university lays claim to being the first established in the Americas. On 28th October 1538, Pope Paul III issued a papal bull recognising a Dominican seminary in Santa Domingo (now in the Dominican Republic) as a university. This institution did not receive official recognition until a royal decree of 1558, when it became known as Universidad Santo Tomás de Aquino (St. Thomas Aquinas University) until its closure in 1832. I leave it to the reader to decide which university has the better claim.