He was the son of the expeditionary José Joaquín Moraga who helped to lead the de Anza Expedition to California in 1774.
The elder Moraga was a member of both expeditions of Juan Bautista de Anza to explore and consolidate the north-western limits of Spain's colonial claims in Alta California.
As a corporal, Gabriel Moraga was appointed comisionado (military administrator) of the Pueblo of San Jose, some years after its establishment by his father in 1777.
Many years after Gabriel Moraga's death, his widow Ana Joaquina Alvarado (1788–1863) was granted (in 1841) the Rancho Cañada Larga o Verde, not far from Mission San Buenaventura.
Gabriel and Ana's son Joaquín was co-grantee of Rancho Laguna de los Palos Colorados in present-day Contra Costa County, part of which is now the city of Moraga, California.