Moresby was born on 29 November 1786 in Calcutta, part of the Bengal Presidency in British India, the son of Mary (née Rotton, 1767-1830) and Lieutenant Colonel (with 2nd Stratfordshire Militia) Fairfax Moresby Sr (1753-1820) of Lichfield.

He joined the Royal Navy in December 1799.
He was assigned to the second-rate HMS London as an able seaman but was promoted to midshipman and took part in the unsuccessful expedition to capture Ferrol in Spain in August 1800 during the French Revolutionary Wars.
He transferred to the first-rate HMS Royal George later that year, to the sixth-rate HMS Alarm in the Channel Squadron in March 1802 and to the fifth-rate HMS Amazon in the Mediterranean Fleet in November 1802.
In HMS Amazon he took part in the pursuit of the French Fleet, under the command of Admiral Pierre-Charles Villeneuve, to the West Indies and back in Summer 1805.
He became mate in the third-rate HMS Puissant at Portsmouth in December 1805 and then transferred to the first-rate HMS Hibernia, flagship of the Earl St Vincent, and saw action during the blockade of Brest during the Napoleonic Wars.

Promoted to lieutenant on 10 April 1806, Moresby was appointed to the first-rate HMS Ville de Paris and, after transferring to the third-rate HMS Kent in 1807, took part in the blockade of Rochefort.
He subsequently transferred to the third-rate HMS Repulse in the Mediterranean Fleet and later to the third-rate HMS Sultan.
He was then made acting commanding officer first of the sloop HMS Eclair and then of the sloop HMS Acorn observing French and Venetian ships in the Adriatic Sea in Spring 1811.
Promoted to commander on 18 April 1811, he became commanding officer of the sloop HMS Wizard and was sent to the Aegean Sea to defend the population of Malta from pirates; the grateful people presented him with a sword.
He then returned to the Adriatic Sea where he led a naval brigade providing artillery support to the Austrian forces during the siege of Trieste in October 1813.
He was appointed a Knight of the Austrian Military Order of Maria Theresa on 23 May 1814 and, having been promoted to captain on 7 June 1814, was appointed a Companion of the Order of the Bath on 4 June 1815.

Moresby became commanding officer of the sixth-rate HMS Menai in April 1819 and went on to be senior naval officer at the Cape of Good Hope early in 1820 and then senior officer at Mauritius in 1821, with orders to suppress the slave trade: he concluded the Moresby Treaty with Seyyid Said, the imam of Muscat in September 1822 restricting the scope of local slave trading and conferring on English warships the right of searching and seizing local vessels.
In one action he boarded the schooner Camilla and freed 140 slaves.
Moresby became commanding officer of the third-rate HMS Pembroke in the Mediterranean Fleet in January 1837 and commanding officer of the third-rate HMS Canopus in the Channel Squadron in March 1845.
Moresby was born on 29 November 1786 in Calcutta, part of the Bengal Presidency in British India, the son of Mary (née Rotton, 1767-1830) and Lieutenant Colonel (with 2nd Stratfordshire Militia) Fairfax Moresby Sr (1753-1820) of Lichfield.
He joined the Royal Navy in December 1799. He was assigned to the second-rate HMS London as an able seaman but was promoted to midshipman and took part in the unsuccessful expedition to capture Ferrol in Spain in August 1800 during the French Revolutionary Wars. He transferred to the first-rate HMS Royal George later that year, to the sixth-rate HMS Alarm in the Channel Squadron in March 1802 and to the fifth-rate HMS Amazon in the Mediterranean Fleet in November 1802. In HMS Amazon he took part in the pursuit of the French Fleet, under the command of Admiral Pierre-Charles Villeneuve, to the West Indies and back in Summer 1805. He became mate in the third-rate HMS Puissant at Portsmouth in December 1805 and then transferred to the first-rate HMS Hibernia, flagship of the Earl St Vincent, and saw action during the blockade of Brest during the Napoleonic Wars.
Promoted to lieutenant on 10 April 1806, Moresby was appointed to the first-rate HMS Ville de Paris and, after transferring to the third-rate HMS Kent in 1807, took part in the blockade of Rochefort. He subsequently transferred to the third-rate HMS Repulse in the Mediterranean Fleet and later to the third-rate HMS Sultan. He was then made acting commanding officer first of the sloop HMS Eclair and then of the sloop HMS Acorn observing French and Venetian ships in the Adriatic Sea in Spring 1811. Promoted to commander on 18 April 1811, he became commanding officer of the sloop HMS Wizard and was sent to the Aegean Sea to defend the population of Malta from pirates; the grateful people presented him with a sword. He then returned to the Adriatic Sea where he led a naval brigade providing artillery support to the Austrian forces during the siege of Trieste in October 1813. He was appointed a Knight of the Austrian Military Order of Maria Theresa on 23 May 1814 and, having been promoted to captain on 7 June 1814, was appointed a Companion of the Order of the Bath on 4 June 1815.
Moresby became commanding officer of the sixth-rate HMS Menai in April 1819 and went on to be senior naval officer at the Cape of Good Hope early in 1820 and then senior officer at Mauritius in 1821, with orders to suppress the slave trade: he concluded the Moresby Treaty with Seyyid Said, the imam of Muscat in September 1822 restricting the scope of local slave trading and conferring on English warships the right of searching and seizing local vessels. In one action he boarded the schooner Camilla and freed 140 slaves. Moresby became commanding officer of the third-rate HMS Pembroke in the Mediterranean Fleet in January 1837 and commanding officer of the third-rate HMS Canopus in the Channel Squadron in March 1845.
Fairfax Moresby