Judges announced Kadare's win on Friday.
Kadare, 69, fled his homeland and was granted political asylum in France in 1990, only a few months before Albania's communist regime ended.
Before that, his French publisher, Editions Fayard, smuggled his work out of Albania, the prize committee said.
"Ismail Kadare is a writer who maps a whole culture - its history, its passion, its folklore, its politics, its disasters," said John Carey, chairman of the judging committee. "He is a universal writer in a tradition of storytelling that goes back to Homer."
Kadare said he hoped the prize, given for his body of work, would give the world a different perspective on the tiny Balkan country and its neighbours.
"I am a writer from the Balkan fringe, a part of Europe which has long been notorious exclusively for news of human wickedness - armed conflicts, civil wars, ethnic cleansing and so on," he said.
"My firm hope is that European and world opinion may henceforth realise that this region ... can also give rise to other kinds of news and be the home of other kinds of achievement, in the field of the arts, literature and civilisation," he said.
Kadare, who writes both poetry and prose, became well known in his homeland with the 1963 publication of his first novel, The General of the Dead Army. Among his other works are The Three Arched Bridge, The Concert and The Palace of Dreams.
The Man Booker International Prize, the creation of which was announced last year, is open to authors of all nationalities whose work has been either written or translated widely into English.
The $109,000, prize will be awarded for a body of work every two years.
Kadare's work includes both
poetry and prose
The annual Man Booker Prize for Fiction is awarded for a single work, and is open only to writers from Britain, Ireland and the Commonwealth of former British colonies.
Among the 18 finalists for the international prize announced in February were Nobel laureates Saul Bellow, Gunter Grass, Gabriel Garcia Marquez and Kenzaburo Oe.
Other finalists included Philip Roth, John Updike, Margaret Atwood, Ian McEwan, Milan Kundera and Doris Lessing.
Kadare will receive his prize at a ceremony in Edinburgh, Scotland, on 27 June.