Wollaston, the son of a clergyman from East Dereham in Norfolk, was educated at Cambridge University, England, where he graduated in 1788. He practiced as a physician before moving to London (1801) to devote himself to science, working in a variety of fields, including chemistry, physics, and astronomy, and making several important discoveries, both theoretical and practical.

Wollaston made himself financially independent by inventing, in 1804, a process to produce pure malleable platinum, which could be welded and made into vessels. He is reported to have made about £30,000 from his discovery, as he kept the process secret until shortly before his death, allowing no one to enter his laboratory. Working with platinum ore, he also isolated two new elements: palladium (1804), named for the recently discovered asteroid Pallas, and rhodium (1805), named for the rose color of its compounds. In 1810 he discovered the second amino acid, cystine, in a bladder stone.

In optics Wollaston developed the reflecting goniometer (1809), an instrument for the measurement of angles between the faces of a crystal. He also patented the camera lucida in 1807. In this device an adjustable prism reflects light from the object to be drawn and light from the paper into the draftsman's eye. This produces the illusion of the image on the paper, allowing him to trace it. Wollaston was a friend of Thomas Young and a supporter of the wave theory of light. One opportunity he missed occurred when, in 1802, he observed the dark lines in the solar spectrum but failed to grasp their importance, taking them simply to be the natural boundaries of colors. He missed a similar chance in 1820 when he failed to pursue the full implications of Hans Oersted's 1820 demonstration that an electric current could cause a deflection in a compass needle. Although he performed some experiments it was left to Michael Faraday in 1821 to discover and analyze electromagnetic rotation. Wollaston was successful in showing that frictional and galvanic electricity were identical in 1801. In 1814 he proposed the term ‘chemical equivalents’.