Kucharova defeated 103 other women in voting by a panel of judges and television viewers around the world during a two-hour finals ceremony in the Polish capital.
First runner-up in the 56th edition of the annual beauty pageant was Joana Valentina Boitor, a 17-year-old from Romania. Australia's Sabrina Houssami, 20, was third.
Wearing a long white dress, a teary Kucharova blew kisses to the 2,500 audience members in Warsaw's Congress Hall after she received her diamond crown from Miss World 2005, Unnur Birna Vilhjalmsdottir of Iceland.
Kucharova, a tall high-school student with long blond hair, was born in Trnava and grew up in the town of Opocno. She told the judges she wants to attend university and then become a model. She likes tennis and horse riding and her personal motto is "Always be an optimist."
A few white-red-and-blue Czech national flags floated in the cheering audience after the verdict was announced.
The organizers of the pageant said this year's finals offered the widest-ever participation of voters around the world via the Internet. Votes were also submitted in text messages sent from mobile phones.
Warsaw is only the second European capital after London to host the Miss World contest, organizers say. The 104 finalists spent the past month touring the Eastern European country's cities, beaches and countryside.
Last month, a white scarf was added to an artist's depiction of a mermaid with an exposed breast on a poster advertising the contest after officials in Warsaw's conservative administration deemed it too suggestive.