Sturgeon's father, a shoemaker of Whittington, England, has been described as an “idle poacher who neglected his family.” Seeing little future as an apprentice cobbler Sturgeon enlisted in the army in 1802. While serving in Newfoundland his interest in science was aroused while watching a violent thunderstorm. Finding that no one seemed able to explain satisfactorily to him the cause and nature of lightning, he started reading whatever science books were available. This led him to the study of mathematics and Latin. When he left the army in 1820 he had acquired a considerable amount of scientific knowledge and skill. He began to write popular articles, joined the Woolwich Literary Society, and must have so impressed his associates that a move was made to find him a more suitable job than the shoemaking he was being forced back into. Thus in 1824 he was appointed to a lectureship in experimental philosophy at the East India Company's Royal Military College at Addiscombe.

In 1840 he moved to Manchester as the superintendent of the Royal Victoria Gallery of Practical Science. In 1836 he began the publication of the Annals of Electricity, the first periodical of its kind to be issued in Britain.

After various further appointments as an itinerant lecturer he was awarded a government pension of £200 a year for his services to science. His collected papers, Scientific Researches, were published in 1850.

Sturgeon made several fundamental contributions to the new science of electricity. The cell devised by Alessandro Volta had certain inherent weaknesses – any impurity in the zinc plates used caused erosion of the electrode. In 1828 Sturgeon found that amalgamating the plate with mercury made it resistant to the electrolyte. More important was his construction in about 1821 of the first electromagnet. Following the work of François Arago he wound 16 turns of copper wire around a one-foot iron bar, which, when bent into the shape of a horseshoe, was powerful enough to lift a weight of 9 pounds when the wire was connected to a single voltaic cell. He demonstrated his magnets in 1825 in London. More powerful ones were soon built by Joseph Henry and Michael Faraday.

In later years Sturgeon also made improvements to the design of the galvanometer, inventing the moving-coil galvanometer in 1836. In the same year he introduced the first commutator for a workable electric motor (1836).