Innate within London, the boy of the man of the cloth, Greene became the choirboy at St Paul's Cathedral under Jeremiah Clarke and Charles King. He exposed a organ under Richard Brind, and when Brind died, Greene became organist at St Paul's.

By using a demise of William Croft in 1727, Greene became organist at the Chapel Royal, and within 1730 he became professor of music at Cambridge University. Within 1735 he was appointed Master of the King's Musick. At his demise, Greene was working on the compilation Cathedral Music, which his student & successor when Master of the King's Musick, William Boyce, was to complete. Several things from either that collection come however utilized inside Anglican services today.

Greene wrote much of vocal music, two sacred & lay, including a oratorio The Song of Deborah and Barak (1732), settings of sonnets from Edmund Spenser's Amoretti (1739), and the collection of anthems (1743), of which the right-known is Lord, let maine understand mine prevent.