He received a thorough musical education from his father, Thomas Greatorex, who was for many years organist of Westminster Abbey, and conductor of the London "concerts of ancient music."
For some years he was organist and conductor of the choir at St. Paul's chapel.
Greatorex did much to advance the standard of sacred music in the United States in the days when country singing-school teachers imposed their trivial melodies and the convivial measures of foreign composers on the texts of the hymn books at hand.
He published a Collection of Psalm and Hymn Tunes, Chants, Anthems, and Sentences (Boston, 1851).
One of Greatorex's best-known compositions is a setting of the Gloria Patri, widely used in Protestant denominations for the singing of the doxology in services to this day.