Sturgeon was born in Whittington in Lancashire and apprenticed to a shoemaker. He joined the army in 1802 and taught himself mathematics and physics. In 1824 he became lecturer in science at the Royal Military College at Addiscombe in Surrey and in the following year he exhibited his first electromagnet. In 1828 he put into practice Ampere's idea of a solenoid.
In 1832 he was appointed to the lecturing staff of the Adelaide Gallery of Practical Science. In 1836 he established the journal Annals of Electricity, and in the same year he invented a galvanometer.
In 1840 he became superintendent of the Royal Victoria Gallery of Practical Science in Manchester. The Gallery closed in 1842, and he earned a living by lecturing and demonstrating. He died in Prestwich.