After being educated at Caius College, Cambridge and awarded a research fellowship at Churchill College, Overy taught history at Cambridge from 1972 to 1979, as a fellow of Queens' College and from 1976 as a university assistant lecturer. In 1980 he moved to King's College London, where he became professor of modern history in 1994. He was appointed to a professorship in Exeter University in 2004.

In the late 1980s, Overy was involved in a historical dispute with the Timothy Mason that mostly played out over the pages of Past and Present journal over the reasons for the outbreak of World War Two in 1939. Mason had contended that a "flight into war" had been imposed on Adolf Hitler by a structural economic crisis, which confronted Hitler with the choice of making difficult economic decisions or aggression. Overy argued against Mason's thesis, maintaining that though Germany was faced with economic problems in 1939, the extent of these problems cannot explain aggression against Poland and the reasons for the outbreak of war were due to the choices made by the Nazi leadership. For Overy, the problem with Mason's thesis was that it rested on the assumption that in a way not shown by records, information was passed on to Hitler about the Reich's economic problems. Overy argued that there was a difference between economic pressures induced by the problems of the Four Year Plan and economic motives to seize raw materials, industry and foreign reserves of neighboring states as a way of accelerating the Four Year Plan. Overy asserted that the repressive capacity of the German state as a way of dealing with domestic unhappiness was somewhat downplayed by Mason. Finally, Overy argued that there is considerable evidence that the German state felt they could master the economic problems of rearmament; as one civil servant put it in January 1940 "we have already mastered so many difficulties in the past, that here too, if one or other raw material became extremely scarce, ways and means will always yet be found to get out of a fix". Recently, another British historian, Adam Tooze, has argued for a similar position as Mason's in his book The Wages of Destruction.

His work on World War II has been praised as "highly effective (in) the ruthless dispelling of myths" (A. J. P. Taylor), "original and important" (New York Review of Books) and "at the cutting edge" (Times Literary Supplement).

Prof. Overy was featured in the 2006 BBC docudrama Nazis on Trial.