Arne's father and grandfather were both upholsterers and both became officials of the City Company of Upholsterers. His grandfather fell upon hard times and died in the Marshalsea Prison for debtors. Arne's father earned enough money not only to rent a large house in Covent Garden but also to have Arne educated at Eton College. But later in life, he also managed to lose most of his wealth and had to earn extra cash by acting as a numberer of the boxes at Drury Lane Theatre.

Arne was so keen on music that he smuggled a spinet into his room and, dampening the sounds with his handkerchief, would secretly practice during the night while the rest of the family slept. He also dressed up as a liveryman in order to gain access to the gallery of the Italian Opera. It was at the opera that Arne first met the musician and composer Michael Festing, who was a major influence on Arne. He not only taught him to play the violin, but also took him to various musical events, including going to hear Thomas Roseingrave compete for the post of organist at Hanover Square and a visit to Oxford in 1733 to hear Handel's opera Athalia.

Upon leaving school, Arne was articled to a solicitor for three years. However, Arne's father discovered his son leading a group of musicians at what was probably one of Festing's musical gatherings. Following this disclosure of his son's real interest and talent, he was persuaded (again probably by Festing) to allow the young Arne to give up his legal career and to pursue music as a living.

He was baptised in the Roman Catholic faith, his mother's religion.

Arne's sister, Susannah Maria Arne, was a famous contralto, who performed in some of his works, including his first opera, Rosamund. (She would later become known professionally as "Mrs Cibber".) They and their brother Richard would often perform Arne's works together. Between 1733 and 1776, Arne wrote music for about 90 stage works, including plays, masques, pantomimes, and opera. Many of his dramatic scores are now lost, probably in the disastrous fire at Covent Garden in 1808.

Arne was a Freemason and active in the organisation, which has long been centred around the Covent Garden area of London, of which Arne was a native.

Arne's Catholicism meant that he never composed music for the Church of England, unlike most other great English composers of his time.

On 15 March 1737, Arne married singer Cecilia Young, whose sister, Isabella was the wife of John Frederick Lampe. Arne's operas and masques became very popular, and he received the patronage of Frederick, Prince of Wales, at whose country home, Cliveden, the Masque of Alfred, featuring "Rule Britannia", was debuted.

In 1741, Arne filed a complaint in Chancery pertaining to a breach of musical copyright and claimed that some of his theatrical songs had been printed and sold by Henry Roberts and John Johnson, the London booksellers and music distributors. The matter was settled out of court. Arne was certainly one of the very first composers to have appealed to the law over copyright issues.

In 1750, after an argument with David Garrick, Susannah left Drury Lane for Covent Garden Theatre, and Thomas followed. In 1755 during a period spent in Dublin, he separated from Cecilia, who, he alleged, was mentally ill. He began a relationship with one of his pupils, Charlotte Brent, a soprano and former child prodigy. Brent performed in several of Arne's works, including the role of Sally in his 1760 opera Thomas and Sally and Mandane in his 1762 opera Artaxerxes. Eventually Brent and Arne went their separate ways and she married a violinist Thomas Pinto in 1766.

During the 1760s Arne frequently collaborated with the Irish writer Isaac Bickerstaff. Thomas and Sally was the first English comic opera to be sung throughout (it contained no dialogue). Artaxerxes was one of the most successful and influential English operas of the eighteenth century and is the only known attempt to write an Italianate, Metastasian opera seria, in the English language. It was frequently performed in London into the 1830s. On 1791 visit to London Joseph Haydn was impressed by a performance of Ataxerses he attended and admitted that he had no idea such an opera existed in the English language.

In 1769 Arne composed the song Soft Flowing Avon, with lyrics by David Garrick, for the Shakespeare Jubilee held by Garrick in Stratford - upon - Avon to commerotate the life of William Shakespeare.

In 1777, shortly before his death, Arne and his wife were reconciled. They had one son, Michael Arne. Arne is buried at St Paul's, Covent Garden, London.