Born and educated in Cap-Santé, Lower Canada, the son of François-Xavier Garneau and Julie-Henriette Gignac, Garneau moved to Quebec City in 1839 to work as a clerk for a fancy-goods merchant.

He eventually worked for his own importing wholesaler called Têtu et Garneau.

He was elected by acclamation to the Legislative Assembly of Quebec for the electoral district of Québec-Comté in an 1873 by-election.

In 1874, he was the commissioner of agriculture and public works in the cabinet of Charles-Eugène Boucher de Boucherville.

In 1887, he was appointed to the Legislative Council of Quebec for the division of La Durantaye.