He was the third and youngest son of William Reece (died 1781), vicar of Bosbury, rector of Coddington, and curate of Colwall in Herefordshire, by Elizabeth Anna Mackafee, lady of the manor of Battleborough, Somerset.

Early devoting himself to the profession of medicine, Richard was at the age of twenty resident surgeon at the Hereford Infirmary.

He secured considerable practice in London, and was consulted by Joanna Southcott, who was then aged 64, as to the possibility of her supernatural pregnancy.

Reece led an active life, and, in addition to his practice, interested himself in therapeutic and chemical pursuits at a time when these studies were but little considered.

Reece published: A miniature in oils, by R. Bull, belonged to Dr. A. J. Richardson of West Brighton.