Educated in Dublin, he was elected an associate of the Royal Hibernian Academy at the age of twenty-one and an academician two years later. In 1842 he began to exhibit at the Royal Academy. A visit to Germany and Bavaria in 1842 was the first of a long series of trips to various parts of Europe, which gave him a profound knowledge of the works of the Old Masters. From 1851 he spent 7 years working as a painter in the service of Maximilian II of Bavaria.
Burton worked with George Petrie on archaeological sketches and was on the council of the Royal Irish Academy and the Archaeological Society of Ireland. He was elected an associate of the Royal Society of Painters in Watercolours in 1855, and a full member in the following year. He resigned in 1870, and was reelected as an honorary member in 1886. A knighthood was conferred on him in 1884, and the degree of LL.D. of Dublin in 1889. In his youth he had strong sympathy with the Young Ireland Party. He died in Kensington, west London and is buried in Mount Jerome Cemetery, Dublin.
The Meeting on Turret Stairs, 1864
Burton's best-known watercolours, The Aran Fisherman's Drowned Child (1841) and The Meeting on the Turret Stairs (1864; also known as Hellelil and Hildebrand) are in the National Gallery of Ireland. Meeting on the Turret Stairs was voted by the Irish public as Ireland's favourite painting in 2012 from among 10 works shortlisted by critics.