Green took the examination for naval cadetships successfully in July 1879 and joined the Royal Navy as a midshipman in 1882. He was promoted to lieutenant on 1 January 1890 and went on to command the gunboat during the Boxer Rebellion in 1900, for which role he was mentioned in despatches and received a special promotion to Commander on 1 January 1901. He was appointed in command of the destroyer on 13 June 1901, and used her as his flagship when he was in charge of the Medway Instructional Flotilla. In May 1902 he transferred with all officers and men of Mermaid to the destroyer, which was commissioned for the instructional flotilla. In 1903, the Admiralty demanded that he explain why he had never conducted torpedo practice while in command of the flotilla and was unimpressed by his explanation. Promoted to captain on 30 June 1906, Green received a commendation in 1907 for efforts he made in helping to salvage the destroyer, which had been wrecked on 19 April 1907 when she ran aground on a breakwater just outside Grand Harbour, Valletta, Malta. He took command of the second-class protected cruiser on 30 May 1908. In late 1908, Forte performed extremely poorly in a gunlayer′s test; a court of inquiry convened to find out the reason for the poor test results faulted Green and the other officers of Forte for failing to provide sufficient training. In 1910, Forte ran aground and the Admiralty expressed "severe displeasure for failure to comply with King's Regulations|K′s R & for unseamanlike manner in which His Majesty's Ship|H M′s ship was navigated." Green left Forte in March 1911. Green was commanding officer of the armoured cruiser from September 1911 to May 1912 and took command of the first-class protected cruiser in October 1912. He took command of the armoured cruiser on 14 May 1913. On 5 June 1913, Natal collided in fog with a fishing vessel. A court of inquiry convened to investigate the collision conclude that Natal′s speed of 10 knots when she struck the fishing vessel was excessive for the foggy conditions, but the Admiralty declined to endorse this finding.
While hunting on 31 October 1925 in Fife, Scotland, with retired Admiral Edward H. Moubray and Admiral Sir Henry Oliver, Commander-in-Chief of the Atlantic Fleet, Green accidentally shot Oliver with one barrel of his shotgun. Oliver was not seriously injured, and later said that it was not the first time that Green had accidentally shot someone and that Green in fact had a reputation for it. While on the retired list, Green was promoted to admiral on 1 August 1927. He died on 30 October 1948.