He was born in East Dereham in Norfolk, the son of the Francis Wollaston (1737–1815), a noted amateur astronomer, and his wife Althea Hyde. He was one of 17 children, but the family was financially well-off and he enjoyed an intellectually stimulating environment. He was educated privately (and remotely) at Charterhouse School from 1774 to 1778 then studied Sciences at Gonville and Caius College, Cambridge. In 1793 he obtained his doctorate (MD) in medicine from Cambridge University, and was a Fellow of his college from 1787 to 1828.
He worked as a physician in Huntingdon from 1789 then moved to Bury St Edmunds before moving to London in 1797. During his studies, Wollaston had become interested in chemistry, crystallography, metallurgy and physics. In 1800, after he had received a large sum of money from one of his older brothers, he left medicine. He concentrated on pursuing his interests in chemistry and other subjects outside his trained vocation.
He was elected a Fellow of the Royal Society in 1793, where he became an influential member. He served as its president in 1820. In 1822 he was elected a Foreign Honorary Member of the American Academy of Arts and Sciences.
Wollaston died in London 28 December 1828 and was buried in St Nicholas's Churchyard in Chislehurst, England.