Topolski was born in Warsaw where he studied at the Academy of Art while also serving as a cadet at the Artillery Officers' School from 1927 to 1932. He spent time studying on his own in France and Italy before being sent to England in 1935 to record George V's Silver Jubilee for a Polish magazine. He stayed in London permanently, frequenting a literary group at the Café Royal that included Graham Greene, Evelyn Waugh, J B Priestley and Anthony Powell. They began to commission illustration for magazines and plays, including Bernard Shaw who used him on three works including an edition of Pygmalion. On the outbreak of war in 1939 Topolski began working as honorary official artist to the Polish forces in Britain before being employed by the War Artists Advisory Committee from 1940 as an official war artist for the British. Given Stalin’s reluctance to allow photographic illustrations of conditions in Russia following the Nazi invasion in the summer of 1941, the British assigned Topolski to accompany the first Allied aid convoy to the Soviet Union. From then he travelled frenetically across all theatres of operations throughout the war, sketching the common soldier and the general staff alike, in Egypt, East Africa, Palestine, Lebanon, Syria, Iraq, India, the Burma Front, China, France and Germany. He was commissioned to record the London Blitz in 1940 and was wounded while sketching. He followed the Polish 2nd Corps in Italy in the fiercest of fighting and was at Bergen-Belsen concentration camp in the weeks after its liberation. One of his final official commissions involved visually recording the proceedings at the Nuremburg Trials. He became a naturalised British citizen in 1947.

In peacetime he attended both the Congress of Europe in The Hague for Vogue magazine and the International Congress of Intellectuals for Peace in Wroclaw, Poland, the resulting drawings for the latter were published as Confessions of a Congress Delegate in 1949. A year later he was invited to India by Prime Minister Jawaharlal Nehru, to record the transition from Raj to Independence and produce a mural 'The East'. The two became great friends and Nehru's daughter, Indira Ghandi, would often visit Topolski's studio when in London.

Throughout the latter half of the twentieth century Topolski established himself as the artistic chronicler of world events. He recorded the liberation conflicts in Malaya and Indo-China, Pope Paul VI’s visit to the Holy Land in 1964 and the start of Mao’s Cultural Revolution in China in 1966. He travelled to America in 1968 and documented the Democratic Convention riots in Chicago, before going to San Francisco to meet members of the Black Panther Party.

He produced two public murals in London, the 'Cavalcade of Commonwealth' for the Festival of Britain 1951 and 'Coronation of Elizabeth II' in 1959. The latter had been commissioned by the Duke of Edinburgh for a corridor in Buckingham Palace. His magnum opus, the 'Memoir of the Century', was a summation in oils of all his memories and records of events that he had witnessed, on dozens of large scale painted panels. Begun in 1975 under the arches of the Hungerford Railway Bridge it was his personal legacy to history and is still looked after by the Topolski Family and the South Bank Centre today.

Twelve of his portraits, including images of H G Wells, E M Forster, Harold Macmillan and Graham Greene are held in the National Portrait Gallery permanent collection. It is testament to the regard to which he was held by his contemporaries that fifteen works in the same collection are portraits of Topolski himself by fellow artists. Feliks Topolski is also represented in the Permanent collections of the British Museum, the Imperial War Museum, the Tate, the V&A and the Museum Narodwe  Warszawie amongst many others. He received an honorary doctorate from the Jagiellonian University in Krakow, Poland in 1974 and the Gold Medal of the International Fine Arts Council in 1955.