The naval architect was born in Hertfordshire.
He became an apprentice at the Elswick shipyard of Armstrong, Whitworth & Co. Later, after a period in Glasgow, Tennyson-D'Eyncourt received in 1902 what he termed 'an irresistible opportunity to go back to the Tyne' when he was invited to take charge of the design office. In 1912 he was appointed director of naval construction in succession to Watts. During his term of office twenty-one capital ships, fifty-three cruisers, 133 submarines of eleven different classes, and numerous other vessels were added to the Royal Navy. The battleships of the Royal Sovereign class were the first capital ship designs for which he was responsible. He introduced the 'bulge' form of protection against torpedo attack and no ship so fitted was sunk in the war of 1914-18 by torpedoes.
In 1915 Tennyson-D'Eyncourt was entrusted with the design of rigid airships for the navy In February of the same year Churchill asked him to undertake the design of a 'landship' which could advance over trenches or wire entanglements. Tennyson-D'Eyncourt was keenly interested in the project and agreed to head a committee formed to design and produce landships or 'tanks' as they were later termed. The prototype was ready for trials early in 1916 and the first tanks saw action at the battle of the Somme.
Among the many naval developments which took place during the war perhaps the most important were those in the design of aircraft-carriers. Under Tennyson-D'Eyncourt's guidance there was rapid progress and a pattern of bridge and superstructure was set which was followed by all other navies. His most impressive design was that of the battle cruiser Hood, the first capital ship to be fitted with small tube boilers, a type he had long advocated. From 1924 to 1928 he was a director of his old firm, Armstrong, Whitworth & Co. He then joined the board of Parsons Marine Steam Turbine Company until his retirement in 1948.