He purchased and donated the land on which the Erskine Presbyterian Church was built, and was president and Governor of the Montreal General Hospital.

Andrew received a classical education at the Paisley Grammar School, and then was instructed in the practical trade of weaving.

In the early 1860s, he built the Auburn Woolen Mill at Peterborough, Canada West, where he manufactured Canadian tweed.

He sold the mill in 1867 in order to buy the future Lord Mount Stephen's wholesale dry goods business in Montreal.

During the American Civil War he joined the Canadian militia as Lieutenant and quartermaster of the Montreal Light Infantry.

In 1881, he journeyed to British Columbia with Sir Charles Tupper, who described Robertson as a "merchant prince," in order to report on the feasibility of the Canadian Pacific Railway building a line between Victoria and Nanaimo.

Andrew also became active in politics and a bi-product of his Tory affiliations was an appointment to the Montreal Harbour Commission by Sir John A. Macdonald in 1878.