Finnbogadóttir was born into a wealthy and well-connected family. Her mother chaired Iceland's national nurses association, and her father was a civil engineer. After graduating from Reykjavík College in 1949, Finnbogadóttir attended the University of Grenoble and the Sorbonne in France and the University of Uppsala in Sweden. She also studied in Denmark and at the University of Iceland, where she later taught French, drama, and theatre history.

From 1972 to 1980 Finnbogadóttir served as director of the Reykjavík Theatre Company (Leikfélag Reykjavíkur) and participated in an experimental theatre group. During that period, she presented French lessons and cultural programming on Iceland State Television, a task that enhanced her national reputation and popularity. During the summer tourist season, she also served as a guide and translator for the Icelandic Tourist Bureau. She became a member of the Advisory Committee on Cultural Affairs in Nordic Countries in 1976 and was elected its chair in 1978.

In 1980, despite being a divorced single mother (she adopted a daughter in 1972), Finnbogadóttir was drafted as a candidate for the presidency of Iceland; she was narrowly elected, with 33.6 percent of the national vote, over three male opponents. She was subsequently reelected three times (1984, 1988, and 1992) before retiring in 1996. Although the Icelandic presidency is largely a ceremonial position, she took an active role in promoting the country as a cultural ambassador and enjoyed great popularity.

In 1996 she became founding chair of the Council of Women World Leaders at the John F. Kennedy School of Government at Harvard University. Two years later she was appointed president of the United Nations Educational, Scientific and Cultural Organization World Commission on the Ethics of Scientific Knowledge and Technology.