Born in London, Wyon was the son of Thomas Wyon senior (1767-1830), medallist and seal engraver. He studied at the Royal Academy and over the next 39 years exhibited over 90 works at their summer exhibition. His sculptures were also displayed at the International Exhibitions of 1851 and 1862 (London) and 1865 (Dublin).

He produced numerous portrait busts of contemporary and historical figures, many of which were reproduced in parian porcelain, by pottery manufacturers, including Wedgwood, Minton, Spode and Worcester, who also commissioned him to produce original figures for production. Wyon also produced architectural reliefs and figures, and designs for medals. Although many of his works were produced in marble, he also worked in bronze.