He was born in September 1826, one of five sons of Donald Paterson (1778-1851), farmer, at Dell of Inshes, Inverness, and Elizabeth Munro(1789–1847).
In 1851 he worked on expanding the Port of Inverness, and from 1854 worked with Joseph Mitchell on the construction of new lines for the Highland Railway, including Inverness to Keith.
Mitchell retired in 1867, and Murdoch became chief engineer of the Highland Railway on 6 November 1874.
[4] As well as engineering the construction of new lines for the Highland Railway, he also prepared the designs of many new stations.
He died on 9 August 1898 whilst still in post, just three months before the opening of the new line from Inverness to Aviemore.