In March 1714 at the age of 17 he began his first musical post as organist at St. Dunstan-in-the-West, Fleet Street.

In the year 1718 Richard Brind died and Greene superseded him as organist at St. Paul's Cathedral. In this post he was responsible for the music at the Cathedral services and also at the annual Sons of the Clergy festival. For this latter event he composed many of his orchestral anthems.About this time Greene married Mary Dillingham

With Talbot Young (1699-1758) Greene was a founder member of the Castle Society. Though not formally established until 1724 this musical organisation existed some years before and was to continue until 1783. When William Croft died in August 1727 Greene was appointed as organist and composer of the Chapel Royal.

Greene had always admired Handel and in Greene's early days at St Paul's he invited Handel to play the great organ there.

Following the death of John Eccles in January 1735 Greene was elected to the highest musical position in the land - Master of the King's Musick. Greene, although not yet 40 years old, now held all the major musical appointments in the country i.e. Organist of St. Paul's Cathedral, Organist and Composer to the Chapel Royal, Professor of Music at Cambridge University and Master of the King's Musick.

This was the year (1743) that saw publication of what many believe to be Greene's finest work - his 40 Select Anthems. It attracted over 133 subscribers for a total of 281 copies. In 1752 Greene inherited the ancestral estate of Bois Hall in Essex making him (for the first time) a wealthy man with an income of £700 per annum. It is assumed that some of this money was spent on a project very close to his heart; to collect church music, ancient and modern, and to present a copy of the finished collection to every cathedral in England.

The composer John Alcock (1715-1806) very generously gave his own collection to Greene. As Hawkins states, Greene unfortunately did not live long enough to complete his wonderful project.

What he bequeathed to Boyce amounted to the most magnificent music library in the country. Boyce carried on Greene's good work, which was eventually published in three volumes between 1760 and 1778 under the title of "The Cathedral Music". Composers represented in the collection include Tallis, Byrd, Morley, Purcell, Gibbons and Blow.

He was buried in the vault of the church of St. Olave's, Jewry where his father had been a minister. Over 100 years later on 18th May 1888, shortly before St. Olave's was to be demolished, the body of Dr. Greene was taken to St. Paul's Cathedral and laid to rest beside the grave of his old pupil, colleague and friend William Boyce.