He was the eldest son of a Presbyterian minister but was adopted by his maternal uncle, Joseph Taylor, who was an army doctor.
Houston completed his apprenticeship in 1824, passing his final examinations and receiving his letters testimonial.
On 19 June 1826, he was elected a member of the Royal College of Surgeons in Ireland days after the sudden death of his mentor Shekleton.
During his 17-year tenure as curator, Houston expanded and catalogued the RCSI museum's extensive specimen collection, described as "one of the most valuable in Europe" by renowned anatomists Friedrich Tiedemann and Jules Germain Cloquet.
[4][5] Houston had a keen interest in teaching, working as an anatomy demonstrator at RCSI in 1824 and in 1837 taking a position as lecturer in surgery at the Park Street School of Medicine.