He was born in East Dereham, Norfolk and in 1793 obtained a doctorate in medicine from Cambridge University. During his studies there he became interested in chemistry, crystallography, metallurgy and physics. In 1800 he left medicine and concentrated on pursing these interests instead of his trained vocation.
Wollaston became wealthy by developing a physico-chemical method for processing platinum ore and in the process of testing the device he discovered the elements palladium in 1803 and rhodium 1804.
During the last years of his life he performed electrical experiments that would pave the way to the eventual design of the electric motor. However, controversy erupted when Michael Faraday, who was undoubtedly the first to construct a working electrical motor, refused to grant Wollaston credit for his earlier work.
Wollaston is also noted for his observations of dark lines in solar spectrum which eventually led to the discovery of the elements in the Sun and for his work on optical devices.
In 1793 he was elected to the Royal Society and served as the Society's Secretary from 1804 to 1816.