Gooch was born at Bedlington, Northumberland and it was at Birkinshaw's ironworks in his native village that he acquired his first skills in engineering. There he met George Stephenson, who knew Birkinshaw well, and his apprenticeship was served in the Forth Street works of Stephenson and Pease in Newcastle. Gooch is commemorated by an inscription at the King's Arms in Bedlington.
In 1837, when he was 21, Gooch was appointed locomotive superintendent of the Great Western Railway, through the recommendation of Marc Isambard Brunel, the engineer father of Isambard Kingdom Brunel (q.v.). This was a post Gooch was to hold for 27 years. He used to regale his Swindon workers with the sentence his mother had repeated to him every morning before he set out for work: 'Ever remember my dear Dan, that you should look forward to being someday manager of that concern!' The GWR was the only one of the regional companies to adopt broad gauge, and in the early days, Gooch was blamed instead of Brunel for the faults of the engines tried on the line. It was Gooch who saved the day for the company with the help of the North Star locomotive (built at the Stephenson works in Newcastle). This was the only reliable machine the company possessed and was chosen to draw the Directors' special train on the opening day in 1841. A 1925 replica of the North Star, 'a marvel of symmetry and compactness' is kept at Swindon, and part of the town is named after it. Gooch used it as the basis for his successful 'Firefly' designs, and so emerged the pattern on which all the great broad-gauge flyers were afterwards based.
Gooch and Brunel became great friends, though very different in temperament. Gooch, for example, disliked the London society circles in which Brunel was at home. In 1861, Brunel appointed Gooch as engineer on the Great Eastern, and the mighty ship sailed for New York on 17 June, with Gooch and his family aboard. After near financial failure, Gooch was instrumental in buying the ship and chartering it for cable-laying. The Great Eastern laid the first transatlantic cable in 1866, and Gooch sent the first cable message across the Atlantic:

Gooch, Heart's Content to Glass, Valentia, 27 July 6 p.m.
Our shore-end has just been laid and a most perfect cable, under God's blessing, has completed telegraphic communication between the Continent and America.

Gooch was made a baronet. Another North East connection here is that the first transatlantic telegraph cables were manufactured by Sir George Elliot (q.v.). Gooch was MP for Cricklade from 1865-85, but in twenty years never said a word in the House of Commons. After serving as its engineer for 27 years, Gooch re-entered the GWR as its chairman and served another 24 years. The company had been on the verge of bankruptcy but Gooch's energy and financial skill were such that it was in a flourishing condition by the time of his death in 1889.