George Stokes was the youngest son of the Reverend Gabriel Stokes, rector of Skreen, County Sligo, Ireland, where he was born and brought up in an evangelical Protestant family. After attending schools in Skreen, Dublin, and Bristol, he matriculated in 1837 at Pembroke College, Cambridge, where four years later, on graduating as senior wrangler and first Smith's prizeman, he was elected to a fellowship. In accordance with the college statutes, he had to resign the fellowship when he married in 1857, but twelve years later, under new statutes, he was re-elected. He retained his place on the foundation until 1902, when on the day before his 83rd birthday, he was elected to the mastership. He did not hold this position for long, for he died at Cambridge on 1 February the following year, and was buried in the Mill Road cemetery.
In 1849, Stokes was appointed to the Lucasian professorship of mathematics at Cambridge, a position he held until his death in 1903. On 1 June 1899, the jubilee of this appointment was celebrated there in a ceremony, which was attended by numerous delegates from European and American universities. A commemorative gold medal was presented to Stokes by the chancellor of the university, and marble busts of Stokes by Hamo Thornycroft were formally offered to Pembroke College and to the university by Lord Kelvin. Stokes, who was made a baronet in 1889, further served his university by representing it in parliament from 1887 to 1892 as one of the two members for the Cambridge University constituency. During a portion of this period (1885–1890) he also was president of the Royal Society, of which he had been one of the secretaries since 1854. Since he was also Lucasian Professor at this time, Stokes was the first person to hold all three positions simultaneously; Newton held the same three, although not at the same time.
Stokes was the oldest of the trio of natural philosophers, James Clerk Maxwell and Lord Kelvin being the other two, who especially contributed to the fame of the Cambridge school of mathematical physics in the middle of the 19th century. Stokes's original work began about 1840, and from that date onwards the great extent of his output was only less remarkable than the brilliance of its quality. The Royal Society's catalogue of scientific papers gives the titles of over a hundred memoirs by him published down to 1883. Some of these are only brief notes, others are short controversial or corrective statements, but many are long and elaborate treatises.