Born at Colooney in Ireland, Higgins worked in London as a young man with his uncle, Bryan Higgins, the chemist. He studied at Oxford University from 1786 and on his return to Ireland became, in 1791, chemist to the Apothecaries Company of Ireland. He moved to Dublin in 1795 to become chemist and librarian to the Royal Dublin Society, this post being made into a professorship in 1800. From 1795 to 1822 he was chemist to the Irish Linen Board.

Higgins is remembered for his contributions to the new atomic theory and for his claim to have anticipated John Dalton. His claim is based on his work A Comparative View of the Phlogistic and Antiphlogistic Theories with Inductions (1789), which was written as a reply to Richard Kirwan's work.

He introduced a clearer symbolism system than that of Dalton but did not follow up his work on atomism until he published a strong attack on Dalton's work in his eight-volume work Experiments and Observations on the Atomic Theory and Electrical Phenomena (1814).

Higgins spent the intervening years between these publications trying to introduce new chemical technology into Ireland. In 1799 he published an Essay on the Theory and Practice of Bleaching, a work written specifically for the bleachers themselves.