Son-in-law Stephen Watson said his father died peacefully in his sleep at Wexham Hospital in Slough, west of London.
Born in London of German-Jewish parents, Winton travelled to Nazi-occupied Czechoslovakia -- which split into the Czech Republic and Slovakia in 1993 -- as a young employee of the London Stock Exchange.
It was there that he organised trains that transported some 669 children, most of them Jews, to Britain in 1939, saving them from concentration camps and near-certain death.
Winton's efforts earned him the nickname "English Schindler" in reference to Oskar Schindler, the German industrialist who rescued hundreds of Polish Jews during the war.
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"A good man, Sir Nicholas Winton, has passed away. He will remain forever a symbol of courage, deep humanity and incredible modesty," Czech Prime Minister Bohuslav Sobotka said on Twitter.
British Prime Minister David Cameron tweeted: "The world has lost a great man. We must never forget Sir Nicholas Winton's humanity in saving so many children from the Holocaust."
He was knighted in 2003, and his Czech supporters have repeatedly petitioned for him to receive the Nobel Peace Prize.