He later served as president of democratic Czechoslovakia and the Czech Republic.
Havel, a former chain smoker who lost half a lung to cancer and had long suffered from poor health, died in his sleep on December 18 at the age of 75.
The government has declared three days of mourning from December 20-22.
President Vaclav Klaus and other officials were the first to sign books of condolences at the Prague Castle on December 19.
The coffin with Havel's body is lying in repose at a desanctified Prague church that Havel and his wife, Dagmar, had turned into a cultural center.
His body will be transferred to Prague Castle to lie in state on December 20.
Czech media say Havel is expected to be buried on December 23.
Tributes have poured in from around the world.
A statement issued by the PEN International writers' association said Havel would "be remembered by all at PEN for his remarkable contribution to literature and his outstanding commitment to freedom of expression."
“Václav Havel was the most courageous fighter for the freedom of speech," said PEN's International Secretary, Hori Takeaki. "He trusted and believed in the ‘power of the powerless’ in the most democratic sense. So many spiritual seeds were planted by him all over the world. He changed the paradigm of global society with his fight for democracy and freedom of speech.”
Within hours of the announcement of his passing, thousands of Czechs and Slovaks paid tribute to Havel in Prague and other cities in the former Czechoslovakia, lighting candles, recollecting memories of the 1989 revolution, and recalling his contributions to the Czech moral fiber.
Slovakia's government has declared a day of mourning on December 23 for Havel, who fought hard to prevent the disintegration of Czechoslovakia and regarded its breakup as a major failure of post-Soviet Czech and Slovak life.