Hamilton's 1956 collage, Just What Is It That Makes Today's Homes So Different, So Appealing?, featuring a bodybuilder holding a lolly with the word pop on it, has been called the first statement of Pop Art.
The British artist, who was famous for his paintings, collages and sculptures, died aged 89 in 2011.
The retrospective includes the painting Swingeing London (1968-69), of Rolling Stone Mick Jagger shielding his face in the back of a police car following a police drugs raid.
Other images of celebrities include Marilyn Monroe and Bing Crosby.
His 2010 work Shock And Awe depicted Tony Blair wearing a cowboy shirt and standing in a burning landscape with a gun on each hip.
Hamilton also designed the plain white cover for the Beatles' White Album of 1968.
The exhibition features his early designs in the 1950s to his final paintings in 2011, while another London gallery, the ICA, is showcasing two Hamilton installations, Man, Machine And Motion (1955) and an Exhibit (1957) to coincide with Tate Modern's retrospective.
Tate also announced that it would be providing thousands of free exhibition tickets to local community groups in the areas around its four galleries.
* Richard Hamilton runs at Tate Modern from February 13 to May 26.
