Charles Eustace Anson was born on 3 December, 1859, a son of the Reverend Frederick Anson, Canon of Windsor and Rector of Sudbury, and the Honourable Caroline Maria, daughter of the fifth Lord Vernon.
Anson was appointed as a naval cadet to the training ship Britannia at Dartmouth and joined the July 1872 term. He would be one of two members of his term to reach flag rank in active service, the other being John Jellicoe.
On 7 August 1882 he was specially promoted to the rank of Lieutenant.
On 17 October 1888, Anson married Maria Evelyn, daughter of Horatio S. J. Ross, in a ceremony at St. Thomas's Church, Portsmouth.
Anson was promoted to the rank of Commander on 30 June, 1895, at the age of thirty-five years, six months, and twenty-seven days.
On 28 December 1900he was appointed in command of the yacht Osborne.
Anson was promoted to the rank of Captain on 31 December 1901.
On 24 November 1904, he was appointed in command of the second class protected cruiser Dido.
He was appointed to command the armoured cruiser Argyll on 24 March 1906, and then moved to become captain of the pre-dreadnought Vengeance on 12 March 1907 until shortly before 20 October 1908, when he was appointed to the Sapphire II in command, as Captain-in-Charge and King's Harbour Master at Portland.
Anson was promoted to the rank of Rear Admiral on 15 May 1911.
On 9 August 1912 Anson became Admiral Superintendent of Chatham Dockyard.
He was succeeded on 9 August 1915, and promoted to the rank of Vice Admiral on 3 April, 1917 and placed on the Retired List at his own request on 13 April. He was advanced to the rank of Admiral on the Retired List on 3 April 1919.
He died on 23 April 1940.