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.