Pueyrredón was born in Buenos Aires, where he was educated at the Royal College, which he left in 1791 to assume the responsibilities for the family business after his father's death. In 1795, he went to Cádiz, Spain, and spent the following years travelling through Spain and France.
When the British occupied Buenos Aires in 1806, Pueyrredón fled to the countryside and rallied a volunteer force which eventually recaptured the city. In 1807 he was sent as representative of Buenos Aires to Spain again, but returned in 1809 via Brazil to Buenos Aires, where he subsequently participated in the independentist movement. After the May Revolution of 1810, which gave birth to the first local government junta, he was appointed governor of Córdoba, and in 1812 he became the leader of the independent forces and a member of the short-lived First Triumvirate. From 1812 to 1815, he was exiled in San Luis.
In 1816, Pueyrredón was elected Supreme Director of the United Provinces of the Río de la Plata. He strongly supported José de San Martín's military campaign in Chile, and also founded the first national bank of Argentina and the national mint. After the declaration of a Unitarian constitution, revolts forced him to resign as Supreme Director in 1819 and go into exile in Montevideo. He subsequently played a very small role in politics, most notably serving in 1829 as a mediator between Juan Manuel de Rosas and Juan Lavalle.
Pueyrredón was married to María Calixta Tellechea y Caviedes. Their only son, famous painter and civil engineer Prilidiano, was born in Buenos Aires on January 24, 1823. From 1835 to 1849, Pueyrredón and his family lived in Europe. He died in retirement on his ranch in San Isidro, Buenos Aires.