George Frederick Armstrong was born on May 15, 1842, in Doncaster, Yorkshire, England.

He was an English engineer and educator specializing in railway, civil, and sanitary engineering. He graduated from King's College, London (1860) and Cambridge University (B.A., 1864; M.A., 1867). Armstrong began his career as an assistant engineer under Richard Johnson, the then Chief Engineer of the Great Northern Railway. By 1869, he returned to work at the company's locomotive works at home in Doncaster and later became engineer of the Isle of Man Railway Company. In 1871, he became the first Professor of Civil Engineering at the Applied Science School of McGill University in Montreal, Quebec, Canada. In 1876, the Chair of Engineering in the then recently founded Yorkshire College at Leeds was established. He accepted the appointment of its first Professor of Engineering, a post he held for about five years. In 1885, Armstrong, who was of Scottish descent, was appointed by the Crown to become the second Regius Professor of Engineering at the University of Edinburgh, a post he held until his death. He inaugurated courses on sanitary engineering for the benefit of the medical students studying public health. He also became an engineering adviser to the Local Government Board for Scotland under the Public Health Act. He was the honorary local secretary for the Institution of Mechanical Engineers, the Iron and Steel Institute and the British Association, as well as the Honorary President of the East of Scotland Engineering Association. He was a member of the Institution of Civil Engineers, a Fellow of the Royal Society of Edinburgh, and a Fellow of the Geological Society of London. Armstrong was President of the Sanitary Engineering Section of the British Institute of Public Health in Edinburgh in 1893. He was elected President of the Royal Scottish Society of Arts in 1896 and became a Fellow at his alma mater, King's College, in 1899. In his final years, Armstrong was an external examiner in engineering at the University of Wales and a member of the Board of Trustees of Wordsworth College. He served as Justice of the Peace for his home county of Westmorland and Chairman of the Grasmere District Council.

In 1893, he married Margaret Anne Brown (1847–1906). He died on November 16, 1900, in Grasmere, Westmorland, England.