On 27 September 1870 he was commissioned into the 1st Yorkshire (West Riding) Artillery Volunteer Corps as a First Lieutenant, a rank replaced by that of Lieutenant during British Army standardisation in 1871. The 1st Yorkshire (West Riding) Artillery Volunteer Corps was a Volunteer Force coastal artillery unit formed at Leeds in 1860 and armed with 32 pounder guns. Elliott-Cooper was promoted to Captain on 5 June 1875 and Major on 16 April 1879.
He resigned his commission as a Major on 27 February 1886 and was permitted to retain his rank and continue to wear the uniform.
On 30 May 1874 Elliott-Cooper applied for a patent for "improvements in apparatus for locking railway signals and switches, and for locking railway signals and gates at level crossings", this patent was granted provisional protection on 26 June 1874. Elliott-Cooper was appointed a tax commissioner for the City of Westminster and its liberties on 9 August 1899.
He returned to the army by serving in the Engineer and Railway Staff Corps, an unpaid volunteer unit which provides technical expertise to the British Army. He was commissioned into this corps as a Lieutenant-Colonel on 6 January 1900 He was awarded the Volunteer Officers" Decoration on 15 November 1904 in recognition of his twenty years service as a volunteer officer
Elliott-Cooper continued in the Engineer and Railway Staff Corps as a Lieutenant-Colonel after that corps" transferral from the Volunteer Force to the newly formed Territorial Force on 1 April 1908.
He was made Commandant of the corps on 27 July 1912 and promoted to the honorary rank of Colonel. He resigned his commission with the corps on 21 March 1914 and was again permitted to retain his rank and wear the uniform. Elliott-Cooper became the Crown Agent Engineer for the construction of railways by the government in British West Africa on the death of Benjamin Baker in 1907.
He was elected president of the Institution of Civil Engineers for the November 1912 to November 1913 session.
He served as chairman of the War Office Committee of Hutted Camps during the First World War, a service for which he was rewarded with an appointment as Knight Commander of the Order of the Bath on 1 January 1919. He was also elected president of the Smeatonian Society of Civil Engineers in 1923.
In marking his 85th birthday in 1930 the journal Nature noted that he was "among the oldest of English engineers". He drew up the plans for the widening of Knowle Locks on the Warwick and Birmingham Canal in the 1930s.
Elliott-Cooper at one point lived at 44 Princes Gate in Knightsbridge.
He died in 1942.
Elliott-Cooper was a member of the British Standards committee which established standards for the use of Portland Cement in 1919.