Born in Munster County, Ireland, he was educated at Trinity College, Dublin, where he became a scholar in 1734, and Bachelor of Arts in 1735. On 15 October 1740 he began to study medicine at Leyden, and on 12 July 1743 graduated Doctor of Medicine
At Dublin. He became a fellow of the King and Queen"s College of Physicians of Ireland in October 1747, and was elected president of the college in 1755. Three years later he left Dublin in consequence of disagreements with other fellows of the college as to the propriety of his prescribing the powder called after Robert James, Doctor of Medicine, a remedy of which the composition was kept secret by the proprietor. He settled as a physician at Brighthelmstone (later called Brighton) in 1759, and in 1761 published A Short History of Brighthelmstone (London, Octavo), then a town of about two thousand inhabitants, of which the main purposes were to give an account of the climate and other advantages of the place as a residence for invalids, and to promote the drinking of mineral waters and seabathing.
Relhan"s publication led to a substantial increase in public interest in drinking mineral water.
Relhan also authored a treatise on the use of music in medicine, and several other medical publications. In 1763, having been incorporated Doctor of Medicine In the same year he published "Refutation of the Reflections against Inoculation".
He delivered at the College of Physicians the Gulstonian lectures in 1765, and the Harveian Oration on 18 October 1770. Relhan used to reside and practise at Brighton during the bathing season, and from 1758 to 1767, he had an office on Southampton Street in London.
He died in October 1776, and was buried in the Marylebone graveyard in Paddington Street, London.
The town of Enfield, New Hampshire, was first named "Enfield" by settlers from Enfield, Connecticut, but the town was renamed "Relhan" in 1766 to honor Doctor Anthony Relhan. Following the Revolution, the town was renamed "Enfield" in 1784.
At Cambridge, he became a candidate or member of the College of Physicians of London, and was elected a fellow on 25 June 1764.
