The artist, whose 1956 collage Just What is it that Makes Today’s Homes So Different, So Appealing? is one of the most recognisable and influential pieces of work in British post-war art, had been working on a major retrospective just days before he died.
Hamilton was one of the key artistic figures of the 1960s, an artist who mixed with everyone from Rene Magritte to The Beatles.
For the latter he designed the cover of their White Album for which, he said, he only received £200.
He also had a big influence on the development of glam rock when Bryan Ferry studied art under him in Newcastle.
Hamilton once called Ferry “his greatest creation” while Ferry in return said of his mentor: “I just loved his art and thought he was so intellectual, so interesting and so cool, all the things I wanted to be.”
Hamilton proved rather more radical a figure than his pupil. His work was often political.
At the height of the Troubles he painted a portrait of the Republican hunger striker Bobby Sands and more recently he has addressed the war in Iraq.
One of his most famous pictures is Swingeing London, his response to the arrest of Mick Jagger and the art dealer Robert Fraser on drugs charges.
Tate director Nicolas Serota said: “Richard Hamilton was one of the most influential and distinctive artists of the post-war period.
“Greatly admired by his peers, including Warhol and Beuys, Hamilton produced a series of exquisite paintings, drawings, prints and multiples dealing with themes of glamour, consumption, commodity and popular culture.
“However, this fascination with the consumer society was highly critical, a moral position that was also evident in his distrust of the political ‘right’, ranging from Mrs Thatcher to Tony Blair and Hugh Gaitskell.
“Hamilton died as he would have wished, working to the end completing a work for his current exhibition in Ireland.”
A spokeswoman at the National Galleries of Scotland called Hamilton “one of the great pioneers of 20th-century art”.
She added: “In a Scottish context, his collaboration with Eduardo Paolozzi was of particular importance and was notable for their shared enthusiasm for popular culture, technology and mass media as sources of artistic inspiration.”