From 1851 to 1859, Rivière was trained by his father. As a youth, he was already very fond of animals, drawing animals from the London zoo at age seven. Briton exhibited for the first time at age eleven, Kitten and Tom Kit and First Sight, both with animal subjects, held at the British Institution. Eight years later, he participated in his second exhibition, now at the distinguished Royal Academy.
Rivière attended Oxford University, Receiving his Bachelor degree in 1866, and his Masters in 1873. In Oxford, Rivière met fellow student Clarence Dobell, who introduced and inspired Rivière to paint by the Pre-Raphaelite style, especially historical paintings. Dobell also introduced to Rivière his sister Mary, who would later become his wife. The couple had a son, Hugh, who eventually became an artist as well.
Not completely satisfied executing Pre-Raphaelite paintings, in 1864, the artist steered away from the said style and returned to animal paintings, which was more lucrative and wholesome for his as an artist. From 1866 to 1871, Rivière was able to rise to recognition and establish himself as an artist.
Although often compared to the exquisite animal painter James Ward, Rivière's primary source of inspiration was in Sir Edwin Landseer's artwork. However, Rivière had a distinctive art style. He was especially praised by the almost human-like emotions displayed by the animals, but not in an exaggerated manner. His paintings were also celebrated by the subtle, at the same time, strong connections by humans and his animal companions. Two excellent examples of these kinds of works are Sympathy and Fidelity.
Rivière was elected as a Royal Academy associate in 1878, and a full member two years later. Despite being highly successful and respected, the artist was said to be quite humble, often preferring to celebrate other artists than to praise his own. As an Academician, Rivière began to produce critically acclaimed, although experimental, classically, and biblically themed oil paintings. When the Academic painting was declining in value, Rivière started to create portraits, to support his wife and seven children. He often included a dog in the composition.
Briton Rivière died in April 1920.