He was the second son of Sir Samuel Armytage, 1st Baronet and his wife Anne Griffith, daughter of Thomas Griffith. In 1758, he succeeded his older brother John as baronet. Armytage was a Member of Parliament (MP) for York from 1761 to 1768. Between 1775 and 1776, he was High Sheriff of Yorkshire.
On 10 April 1760, Armytage married Anna Maria Wentworth, eldest daughter of Godfrey Wentworth at St Marylebone Church in London. They had three daughters and three sons, of whose George, the oldest succeeded to the baronetcy.
- Godfrey Wentworth Wentworth (1773–1834), MP, third son of Sir George Armytage, 3rd Baronet, married in 1794 Amelia, daughter of Walter Ramsden Beaumont Fawkes and sister of Walter Fawkes.
- "Leigh Rayment - Baronetage". Retrieved 4 April 2009.
- "ThePeerage - Sir George Armytage, 3rd Bt". Retrieved 12 February 2009.
- Kimber, Edward (1771). Richard Johnson, ed. The Baronetage of England: Containing a Genealogical and Historical Account of All the English Baronets. vol. III. London: Thomas Wotton. p. 112.
- "Leigh Rayment - British House of Commons, York". Retrieved 4 April 2009.
- Burke, John (1832). A Genealogical and Heraldic History of the Peerage and Baronetage of the British Empire. vol. I (4th ed.). London: Henry Colburn and Richard Bentley. p. 43.
- Debrett, John (1824). Debrett's Baronetage of England. vol. I (5th ed.). London: G. Woodfall. p. 443.
- "Wentworth, Godfrey Wentworth (1773–1834), of Woolley Park, nr. Wakefield, Yorks., History of Parliament Online". Retrieved 20 May 2017.
|Parliament of Great Britain|
|Member of Parliament for York
1768 – 1768
With: Robert Lane
Lord John Cavendish
|Baronetage of Great Britain|
1758 – 1783
George Armytage, 4th Baronet