Cooper was born at Canterbury, Kent, and as a small child he began to show strong artistic inclinations, but the circumstances of his family did not allow him to received any systematic training. By the time he was twelve years old, he was working in the shop of a coach painter. Later he obtained a job as a scene painter; and he alternated between these two occupations for about eight years. He still felt a desire to become an artist, and all his spare moments were spent drawing and painting from nature. At the age of twenty he went to London, drew for a while in the British Museum, and was admitted as a student of the Royal Academy.
He then returned to Canterbury, where he was able to earn a living as a drawing-master and by the sale of sketches and drawings. In 1827 he settled in Brussels; but four years later he returned to London to live, and by showing his first picture at the Royal Academy (1833) began an unprecedentedly prolonged career as an exhibitor. Cooper's name is mainly associated with pictures of cattle or sheep, a fact that earned him the epithet 'Cows Cooper'. Cooper collaborated with Frederick Richard Lee R.A. on several paintings, Lee undertaking the landscapes, and Cooper adding animals to complete the scene.
Examples of Cooper's work include:
Cooper was elected an Associate of the Royal Academy (ARA) in 1845 and Royal Academician (RA) in 1867.
The largest public collection of Cooper paintings is owned by Canterbury City Council and housed at the Royal Museum and Art Gallery (Beaney Institute) in Canterbury. Examples are also held by the Tate Gallery, London, and the Victoria and Albert Museum, London, and other public collections, mainly in Britain.
Cooper was a great philanthropist in Canterbury, and used some of his wealth to build a number of Alms Houses for the poor in Chantry Lane in the centre of the city. Most notably in 1882 he developed his private art lessons into a fully-fledged art school in Canterbury, located at his home and studio in St Peter's Street. Originally called the Canterbury Sidney Cooper School of Art, Cooper's art school is still in existence although it is now called the University of Creative Arts. Amongst Cooper's more well-known students was Mary Tourtel, creator and illustrator of the Rupert Bear books for children.
Cooper wrote his reminiscences, under the title of My Life, in 1890.