Born in British India, Geddes was the son of Auckland Campbell Geddes, of Edinburgh, Scotland, and the elder brother of Auckland Geddes, 1st Baron Geddes. He was educated at Oxford Military College and Merchiston Castle School, Edinburgh, until asked to leave.
Geddes then spent 2 1⁄2 years drifting between jobs like lumberjack and steelworker in the United States, eventually becoming a stationmaster for the Baltimore and Ohio Railroad, rising to car-tracer. When he abruptly returned home, his older sister gave him a firm talking-to; late in 1895 he was sent to India for a minor job in estate management, where he built light railways before moving to the Rohilkund and Kumaon railway; he became superintendent in 1901. Returning to England because of his wife's poor health, he joined the North-Eastern Railway, and rose to be deputy general manager in 1911.
During the First World War Geddes was one of the "men of push and go" brought into government service by Minister of Munitions David Lloyd George. Made responsible for small arms production, he established rational goals for rifles, light and heavy machine guns, and production then soared, making many more automatic weapons than the army had requested. Shell production was also booming but these were not adequately getting filled with explosive, and so Geddes was made responsible for them in December 1916; within six months the number of filled shells increased tenfold to two million per week, and the filled shells piled up on French docks. Lloyd George, now Minister of War, persuaded Sir Douglas Haig, Commander of the British Expeditionary Force, to invite Geddes and his three-man team over for two days in August 1916 to advise on transportation. Haig was so impressed that the visit was extended to a month and then Geddes was appointed Director General of Military Railways and Inspector-General of Transportation with the rank of major general. They got the ports and railways working efficiently and built light railways to bring materials to the front. He was knighted in 1916 and appointed a Knight Commander of the Order of the Bath and Knight Grand Cross of the Order of the British Empire in 1917. He was promoted to inspector general of transportation in all theaters of war.
The German U-boat campaign unleashed unrestricted attacks in February 1917. As the British merchant fleet was suffering, Lloyd George transferred Geddes to the Admiralty as Civilian Lord with the rank of vice-admiral. He was given control of British shipbuilding, charged with making up for as many of the losses as possible. He found the Admiralty in disarray and wrote to his friend Field Marshal Haig about the lack of drive. On 19 June 1917 First Sea Lord Jellicoe confessed to the War Cabinet that they were losing. Haig and Geddes breakfasted with Lloyd George to demand a new administration in the Admiralty.
On 6 July 1917 Geddes, strongly recommended by Haig, returned to civilian life as First Lord of the Admiralty. To serve he had to be a member of the House of Commons and was elected in a by-election for Cambridge. He was sworn into the Privy Council the same month. The Daily Telegraph's naval correspondent, Sir Archibald Hurd, later wrote of Geddes and Lloyd George, "No men more ignorant of naval affairs were ever associated together than the Prime Minister and Geddes". Regardless of this deficiency he infused the Admiralty with determined energy, encouraged innovation, openness and initiative. Convoying was turning the tide. Geddes appointed the Belfast shipbuilder Lord Pirrie as controller-general of merchant shipbuilding, and brought William Henry Bragg into the Admiralty to oversee antisubmarine science: they were working with the French to develop sonar which was ready just when the war ended. Jellicoe was replaced at the end of 1917. Convoys in home waters lost only 1.25 percent of their ships, and 2,084,000 American soldiers reached Europe; only 113 were lost to U-boats, despite the German Admiralty's boast that they would destroy them all. At war's end the world supply of shipping was larger than it had been at the outset, thanks to the growth of the Japanese and American merchant fleets. It was a great Allied victory.
Lloyd George's evaluation was that Geddes was "... one of the most remarkable men which the State called to its aid ..." He left the Admiralty in January 1919 and was made a Knight Grand Cross of the Order of the Bath. Lloyd George then asked him to organize a new Ministry of Transport. Until the bill setting up this new office was passed in May 1919, he remained in the cabinet as minister without portfolio. In May 1919 he was appointed the first Minister of Transport. The new ministry was given control over railways, roads, canals and docks but was criticized in both houses of parliament for giving in to nationalization and for its large size. In the autumn of 1921 the handing back of the railways from state control to the companies was being reviewed, which put the Ministry of Transport under further pressure. Geddes had neither taste nor aptitude for political infighting, he resigned in November 1921. He chaired the committee on National Expenditure which proposed heavy cuts in public expenditure to match falling national income, the austerity policy became known as Geddes Axe. When enacted it depressed the economy further. He resigned from the government and the Commons in 1922, becoming director of Dunlop Rubber. From 1924 until his death he was chairman of Imperial Airways.
Geddes' memorable quotation is "We shall squeeze the German lemon until the pips squeak!" which he introduced in a stump speech before the election of 1918. It became a major rallying call during the coalition's campaign.
Geddes married Gwendolen, daughter of Reverend A. Stokes, in 1900. They had three sons, including Sir Reay Geddes, former chairman of the Dunlop Rubber Company. Sir Eric Campbell Geddes died in June 1937, aged 61, after several years of declining health.