Greenhill was a nephew of
Thomas Greenhill. His father, William (one of a family of thirty-nine children by the same father and mother), was a counsellor-at-law, who lived first in London and then retired to a family estate at
Abbot's Langley, Hertfordshire, where Joseph was born and baptised in February 1703–4. He was educated at
Sidney Sussex College, Cambridge, graduated B.A. in 1726, and was admitted M.A. in 1731. Greenhill was appointed rector of
East Horsley in 1727, and of
East Clandon in 1732, both livings in the county of Surrey, and small both as to population and emolument. He lived at East Horsley, and died there in March 1788. ==Works==