Edgeworth was born in Pierrepont Street, Bath, England, son of Richard Edgeworth senior, and great-grandson of Sir Salathiel Lovell through his mother, Jane Lovell, granddaughter of Sir Salathiel.

He anticipated the caterpillar track with an invention that he played around with for forty years but that he never successfully developed.

Edgeworth was a member of the Lunar Society, an informal organisation of Birmingham-based industrialists, scientists and intellectuals that met regularly to discuss and share ideas relating to their fields of interest.

Richard Edgeworth and his family lived in Ireland at his estate at Edgeworthstown, County Longford, where he reclaimed bogs and improved roads.

He sat in Grattan's Parliament for St Johnstown (County Longford) from 1798 until the Act of Union in 1801, and advocated Catholic Emancipation and parliamentary reform.