In India, Stoppard received an English education. His mother Martha married a British army major named Kenneth Stoppard, who gave the boy his English surname. The family eventually moved to England in 1946.

Stoppard left school at seventeen and began work as a journalist for Western Daily Press. By 1960 he had completed his first play A Walk on the Water, which was later produced as Enter a Free Man. From September 1962 until April 1963, Stoppard worked in London as a drama critic for Scene, writing reviews and interviews both under his name and under the pseudonym William Boot (taken from Evelyn Waugh's Scoop).

By 1977, Stoppard had become concerned with human rights issues, in particular with the situation of political dissidents in Central and Eastern Europe. In February 1977, he visited Soviet Union with a member of Amnesty International. In June, Stoppard met Vladimir Bukovsky in London and travelled to Czechoslovakia (then under communist control), where he met Václav Havel, at that time a dissident playwright. Stoppard became involved with Index on Censorship, Amnesty International, and the Committee against Psychiatric Abuse and wrote various newspaper articles and letters about human rights. Stoppard was also instrumental in translating Havel's works into English. The Tom Stoppard Prize was created in 1983 (in Stockholm, under the Charter 77 Foundation) and is awarded to authors of Czech origin. Recently (in August 2005) Stoppard visited Minsk to give a seminar on playwriting, and to learn first-hand about various human rights and political problems in Belarus.

He was appointed CBE in 1978 and knighted in 1997. He has been co-opted into the Outrapo group. He has been married twice, to Jose Ingle (1965-72), a nurse, and to Miriam Moore-Robinson, (1972-92), whom he left to begin a relationship with actress Felicity Kendal. He has two sons from each marriage.