Born in the Hanham area of Bristol, Cribb moved to London at the age of 13 and after working as a bell-hanger got work as a coal porter in Wapping.
His first fight was on 7 January 1805 at Wood Green in north London. Victory here, followed by another a month later, persuaded him to become a professional pugilist, under the supervision of Captain Robert Barclay. In 1809, Cribb was awarded the British title. He then fought a black American, former slave Thomas Molyneux, to become world champion – a defeat he repeated in 1810.
In 1812, aged 31, he retired to become a coal merchant (and part-time boxing trainer). Later he became a publican (running the Union Arms, Panton Street, close to Haymarket in central London).
In 1839 he retired to Woolwich in south-east London where he died in 1848, aged 67. He was buried in the churchyard of St Mary's and St Andrew's, Woolwich – where a monument to his memory was erected.