Born in San Miguel de Horcasitas in what is now the Mexican state of Sonora, three year old Ignacio left with his parents Corporal Domingo Alviso and Angela Trejo, brothers and sister in 1775 on the de Anza Expedition to San Francisco. His father died a year following their arrival. He served as a soldier in the San Francisco Company from 1805 to 1819. In 1838 he was granted Rancho Rincon de Los Esteros. He died in 1848 leaving a large estate.
Ignacio Alviso is the uncle of José María Alviso, an early alcalde of San Jose. He is also the grandfather of Valentine Alviso, who was a member of the California State Assembly (14th District) from 1881-1883.