Stoney, the son of an impoverished landowner, was born at Oakley Park (now in the Republic of Ireland) and educated at Trinity College, Dublin. After graduation in 1848 he worked as an assistant to the astronomer, Lord Rosse, at his observatory at Parsonstown until 1853 when he was appointed professor of natural philosophy at Queen's College, Galway. However, from 1857 onwards Stoney worked as an administrator, first as secretary of Queen's University, Belfast, and finally, from 1882 until 1893, as superintendent of civil service examinations.

Stoney is best known for his introduction of the term ‘electron’ into science. Although he is reported to have spoken of “an absolute unit of electricity” as early as 1874, his first public use of the term in print was in 1891 when he spoke of “these charges, which it will be convenient to call electrons” before the Royal Society of Dublin.

He did however make more substantial contributions to science than this and in early spectroscopy his work was of considerable significance. He began, in 1868, by making a crucial distinction between two types of molecular motion. There was the motion of a molecule in a gas relative to other molecules, which Stoney was able to exclude as the cause of spectra. There was also internal motion of a molecule, which according to Stoney produces the spectral lines. He went on to tackle, with little real success, the difficult problem of establishing an exact formula for the numerical relationship between the lines in the hydrogen spectrum. This problem was solved by the quantum theory of Niels Bohr.