Born in 1789 in Santo Angel Custodio, in the South American territory of Misiones Orientales, his father, Diego de Alvear y Ponce de León, had been posted as a commissioner of the second session to demarcate the borders between Spain and Portugal.
In 1804, at the age of 15 while he was returning to Spain with his family, he saw – having almost arrived in Cadiz – from the flagship La Medea in which he had travelled with his father, how his his mother and seven siblings perished aboard the frigate Mercedes – one of the other ships in same squadron – in the Battle of Cape Santa María, when they were attacked by the English before arriving in Cadiz. He was captured and taken with his father to Great Britain.
On his return to Spain, and after completing the military training that he had begun in Argentina, he participated in numerous campaigns against Napoleon's troops.
In 1809 he arrived in Cadiz where, a few months later, he founded a secret society called "Lautaro", which José San Martin would later join. Not long after, he asked to be discharged from the Spanish army in order to return to Argentina, his homeland.
In Buenos Aires he joined the movement for independence, promoting a new national constitutional assembly in which he served as minister, representing Corrientes, the state in which he was born. He was elected first president and minster of the Assembly of the year 1813, in which he introduced important social reforms, among which were the abolition of slavery and the suppression of all the titles of the nobility [from the colonial period].
Alvear took part in military campaigns and was particular outstanding at the siege of Montevideo against the royalists, and at the great victory at the Battle of Ituzaingó against the Brazilian Empire. He also held political posts in the fledgling republic as well as being sent on diplomatic missions to the United States and Colombia.
He died of acute pneumonia in 1853 in New York.