Boag was born in Paisley, Renfrewshire, Scotland. He emigrated to Australia with his wife and four children in 1853, and arrived in Tasmania after three months in the Victorian gold fields. He worked at several local breweries before entering into partnership with his son James Boag II to run Esk Brewery. The brewery later became what is now known as Boag's Brewery.
He died at age 86 in Melbourne. His remains were transported to Launceston, Tasmania for the Funeral Service, which was held at St Andrew's Church. The cortege comprised a very large number of followers according to a report in The Examiner.