Briton Rivière RA was born in London on 14^th August 1840, the son of William Rivière who was a drawing master at Cheltenham College and then an art teacher at the University of Oxford.  The family were of Huguenot descent. He exhibited a variety of paintings at the Royal Academy but devoted much of his life to animal paintings.

Briton was educated at Cheltenham College and Oxford, where he took his degree in 1867. For his art training he was indebted almost entirely to his father. His paternal uncle Henry Parsons Rivière (1811–1888) was also a noted watercolourist, exhibiting works at the Royal Watercolour Society, London and the Royal Birmingham Society of Artists. His first pictures appeared at the British Institution, and in 1857 he exhibited three works at the Royal Academy, but it was not until 1863 that he became a regular contributor to the Academy exhibitions.

Early in his career, Rivière made some mark as an illustrator, beginning with Punch magazine. He was elected an Associate of the Royal Academy of Arts in 1878, and a Royal Academician in 1881, and received the degree of Doctor of Civil Law at Oxford in 1891. He was narrowly defeated in the election for President of the Royal Academy in 1896. His wife, Mary Alice Rivière, whom he married in 1867, was also a painter and exhibited briefly at the Royal Academy of Arts in 1869–70.  After his death in London in 1920 she presented the British Museum with four of his drawings.

The artist and his wife had seven children; five sons and two daughters. One of the sons, Hugh Goldwin Rivière (1869–1956), became a portraitist.