Dadd was born at Chatham, Kent, England, the son of chemist Robert Dadd (1788/9–1843) and Mary Ann (1790–1824), daughter of shipwright Richard Martin. He was educated at King’s School, Rochester where his aptitude for drawing was evident at an early age, leading to his admission to the Royal Academy of Arts at the age of 20. He was awarded the medal for life drawing in 1840. With William Powell Frith, Augustus Egg, Henry O’Neil and others, he founded The Clique, of which he was generally considered the leading talent. He was also trained at William Dadson’s Academy of Art.

In July 1842, Sir Thomas Phillips, the former mayor of Newport, chose Dadd to accompany him as his draughtsman on an expedition through Europe to Greece, Turkey, Southern Syria and finally Egypt. In November of that year they spent a gruelling two weeks in Southern Syria, passing from Jerusalem to Jordan and returning across the Engaddi wilderness. Toward the end of December, while travelling up the Nile by boat, Dadd underwent a dramatic personality change, becoming delusional, increasingly violent, and believing himself to be under the influence of the Egyptian god Osiris. His condition was initially thought to be sunstroke.

In hospital, Dadd was encouraged to continue painting, and in 1852 he created a remarkable portrait of one of his doctors, Alexander Morison, which now hangs in the Scottish National Portrait Gallery. Dadd painted many of his masterpieces in Bethlem and Broadmoor, including The Fairy Feller’s Master-Stroke, which he worked on between 1855 and 1864. Dadd was pictured at work on his Contradiction: Oberon and Titania by the London society photographer Henry Hering. Also dating from the 1850s are the 33 watercolour drawings titled Sketches to Illustrate the Passions, which include Grief or Sorrow, Love, and Jealousy, as well as Agony-Raving Madness and Murder. Like most of his works, these are executed on a small scale and feature protagonists whose eyes are fixed in a peculiar, unfocused stare. Dadd also produced many shipping scenes and landscapes during his hospitalization, such as the ethereal 1861 watercolour Port Stragglin. These are executed with a miniaturist’s eye for detail which belie the fact that they are products of imagination and memory.

Angela Carter wrote Come unto these Yellow Sands, a radio-play based on Dadd’s life, first broadcast in 1979.

In 1987 a long-lost watercolour by Dadd, The Artist’s Halt in the Desert, was discovered by Peter Nahum on the BBC TV programme Antiques Roadshow. Made while the artist was incarcerated, it is based on sketches made during his tour of the Middle East, and shows his party encamped by the Dead Sea, with Dadd at the far right. It was later sold for £100,000 to the British Museum.

Freddie Mercury was inspired to write the song ‘The Fairy Feller’s Master-Stroke’ based on Dadd’s painting, which he had seen at the Tate Gallery. In 2013 Neil Gaiman wrote an essay about the painting for Intelligent Life (now called 1843 magazine).