Born in Glasgow, Scotland, he arrived in Sydney, Australia (at that time the principal city of the British colony of New South Wales) in 1855. He spent most of his life employed by the NSW Education Department. He was also heavily involved with the Scottish Presbytarian Church and in the organisation and execution of choir events.
He composed the tune "Advance Australia Fair" in 1878 under the pseudodnym of Amicus. It was first sung by Andrew Fairfax in Sydney on St Andrew's Day (November 30) that year at a Highland Society function. The song quickly gained popularity and an amended version was sung by a choir of 10,000 at the inauguration of the Australian Commonwealth in 1901. In 1907, the Australian Government awarded McCormick £100 for having composed it.
McCormick died of old age in 1916 and was buried at Rookwood Cemetery, Sydney.
A puzzling aspect about McCormick is that no picture of him seems to exist.