Yelloly was born at Alnwick, Northumberland, and was the youngest and sole survivor of seven children.

In 1806 he married the daughter of Samuel Tyssen of Narborough Hall, Norfolk, by whom he left children.

Yelloly and published in the Philosophical Transactions for 1829 "Remarks on the Tendency to Calculous Diseases", a work based on the museum of stones extracted from the bladder in Norwich Hospital.

He published a further work on the same subject in 1830, and a pamphlet On Arrangements connected with the Medical Relief of the Sick Poor in 1837.

He read before the Royal Medical and Chirurgical Society seven papers, of which two deal with paralysis due to tumour of the brain.