Finlayson initially studied Arts at the University of Glasgow in the 1856-1857 session. After a few years working in business with his father, he decided on a career in medicine, beginning his studies at Anderson's College in 1862 and moving to Glasgow University in 1863. He graduated MB, CM in 1867. He received his MD two years later.

He was assistant to Sir William Tennant Gairdner in 1871 while Gairdner was Regius Professor of Medicine at Glasgow. In 1875 Finlayson became Physician of the Glasgow Western Infirmary, a post he held until his death.

In 1877 he was elected as Honorary Librarian of the Faculty, a position he held for 25 years. He was President of the Faculty from 1900 to 1903.

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