Spanish librarian and man of letters. He studied Philosophy and Theology, and he taught Ecclesiastical Discipline, Natural Law and People's Law, and Literary History in the Royal Studies of San Isidro.

He joined the San Isidro Library on 11 September 1789, becoming the director librarian in 1814, then, in 1815, he became an academic at the Royal Spanish Academy, although he remained as a supernumerary, and did not become a full member until 1818. He was also an honorific member of the Latin Academy of Madrid.

On the 7th of November 1822 the Central University was inaugurated, with headquarters in the Royal Studies, and having Arrieta as its first librarian director. Unfortunately, it didn't last for a long time, due to a new French invasion which made Ferdinand VII the new absolutist King, and the provision that allowed the creation of the university was revoked. In 1823, the Jesuits got back the Imperial College, but García Arrieta abandoned his position, and he was pressured to exile in France until his death in 1835. Due to the implications in the Constitutional Triennium, in 1824, he was forced to give up his position as a librarian. Of his life in the years that followed until his death in Paris in 1835, we only know his literary works such as the Obras escogidas de Cervantes (Paris, 1826 and 1827).

He was translating several works in French and Italian, as well as the Ecclesiastica Laws of the New Testament, translation from Italian to Spanish (Madrid, Benito Cano, 1793) and the Introduction to the Holy Scripture, translation from the French Bernard Lamy (Madrid, Benito Cano, 1795) serving as study books in the Studies of San Isidro; German comedies (although it was just because there were French versions already), such as La misantropía y el arrepentimiento, of August von Kotzebue (Madrid, Fermín Villalpando, 1800), and El Conde de Olsbach, by Johann Christian Brandes (Madrid, Bernito García, 1801); and compilations of maxims or aphorisms taken from the works of Fenelon (The Adventures of Telemachus, Madrid, 1796) and Cervantes (The Spirit of Miguel de Cervantes Saavedra, Madrid, 1814, and Paris, 1827).