He was born in Eton, Buckinghamshire and educated at Eton College and King's College, Cambridge.(BA, 1726, MA, 1730 and DD, 1743).
He was a Fellow of the Society of Antiquaries of London and in 1768 was elected a Fellow of the Royal Society as a "Rector of Buckland in Hertfordshire, Author of the Greek Thesaurus lately published, and Fellow of the Society of Antiquaries of London, a Gentleman well skilled in Natural History and every branch of Polite Literature". 
He was appointed Garrison Chaplain at Portsmouth barracks in 1775.
Morell is important for having written the longest and most detailed surviving account of collaboration with Handel.
He died in 1784 and was buried in Chiswick, London.
He is best known as the librettist of the following of George Frideric Handel's oratorios:
- Judas Maccabaeus (1747).
- Joshua (1747).
- Alexander Balus (1748).
- Theodora (1750).
- The Choice of Hercules (1750). Uncertain if Morell was the librettist.
- Jephtha (1752).
- The Triumph of Time and Truth (1757). Morell was probably the librettist.
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