Alexander Murray was born on June 2, 1810, in Crieff, Perthshire, Scotland.

He was a geologist and explorer. In 1824, he was enrolled at the Royal Naval College, Portsmouth, and joined the Royal Navy in 1825. During his career in the navy, he was wounded at the Battle of Navarino and received a medal for his actions in 1827. He became a lieutenant in 1833, retired from service in 1835, and immigrated to Woodstock, Upper Canada. In 1836, he purchased farmland and planned to support his family by farming. Unfortunately, severe economic depression and the Rebellions of 1837–1838, caused the family to return to England in 1841. Murray studied geology and received an appointment to the Geological Survey of Great Britain in 1842-1843. In 1843, he was appointed assistant provincial geologist of the Canadian Survey and moved back to Canada to begin geological mapping of the Ontario Peninsula. In 1851, he conducted fieldwork in the Gaspé peninsula and later in Canada West. In 1864, Murray moved to Newfoundland and became the first director of the Geological Survey of Newfoundland. He produced the first geological map of Newfoundland and his reports of rich resources in the island's interior were an important factor in the decision to build the trans-island railway in 1881.

In 1837, he married Fanny Cooper Judkins (1818–1861), and in 1868, he married Elizabeth Eliza A. Cummins (1838–). He died on December 18, 1884, in Crieff, Perthshire, Scotland.