Frank Roberts was born in Buenos Aires on 27 October 1907, the son of Henry George Roberts, the manager of Lever Brothers Limited [later Unilever] in Argentina, and Gertrude Roberts (née Kenyon). He was educated at Bedales School (Hampshire), then at Rugby School and at Trinity College, University of Cambridge. In 1937 he married Celeste Leila Beatrix (died 1990) the daughter of late Sir Said Shoucair Pasha. They had no children.

Roberts had a long and successful diplomatic career. He entered the Foreign Office in 1930 serving first at the Embassy in Paris [France], (1932-35) and at Cairo [Egypt] (1935-37). Following that his diplomatic postings included: Foreign Office (1937–45); Chargé d’Affaires to the Czechoslovak Government (1943); British Minister in Moscow (1945-47); Principal Private Secretary to Secretary of State for Foreign Affairs (1947-49); Deputy High Commissioner in India (1949-51); Deputy-Under Secretary of State, Foreign Office, (1951-54); Ambassador to Yugoslavia [later Bosnia and Herzegovina, Croatia, Kosovo, North Macedonia, Montenegro, Serbia, and Slovenia] (1954-57); UK Permanent Representative on the North Atlantic Council (1957-60); Ambassador to the Soviet Union (1960-62) and then to the Federal Republic of Germany (1963-68).

Roberts also held a number of positions within other organisations and was a Director of Hoechst (UK) and Daimler-Benz (UK). He was Chairman (1970-73), President (1973-83), then Vice-President of the European Atlantic Group (1983-); President of the Atlantic Treaty Association (1969-73); and also President of the Atlantic Council of UK (formerly British Atlantic Committee) (1968-81).

Roberts died on 7 January 1998.