He was born in the Covent Garden area of London, to a family that had prospered in the upholstery business. He was educated at Eton College, and was interested in music from his earliest youth. His sister, Susannah Maria Arne, was a famous contralto, who performed in some of his works, including his first opera, Rosamund, performed in 1733. He taught her to sing, and she first performed with him in 1732, along with their brother Richard. In 1736, Arne married singer Cecilia Young, whose sister, Isabella, married the composer 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 first performed.
In 1750, after an argument with David Garrick, Susannah left Drury Lane for Covent Garden Theatre, and her brother followed. In 1755, he separated from his wife, who, he alleged, was mentally ill. He had in the meantime begun a relationship with one of his pupils, Charlotte Brent, a soprano and former child prodigy, who performed in some of his works. She later married a violinist. In 1777, shortly before his death, Arne and his wife were reconciled. They had one son, Michael Arne.
He is buried at St Paul's, Covent Garden, London.