PRAGUE (Reuters) - Czechs will hold their first presidential election on January 11 and 12 to replace outgoing euroskeptic leader Vaclav Klaus, the speaker of the upper house of parliament said on Monday.

Up to now, the country's parliament has chosen the president. But the assembly agreed to hand that power over to the electorate amid calls for more open democracy, fuelled by a growing public perception of cronyism and corruption in the country's political parties.

Opinion polls suggest the leading candidates to replace Klaus are former prime ministers Milos Zeman and Jan Fischer, in office from 1998-2002 and 2009-2010, respectively.

Both men are much more in favor of closer cooperation with the European Union than Klaus. Both were members of then Czechoslovakia's totalitarian Communist party before the collapse of the Soviet Union.

Fischer is running as an independent candidate while Zeman has the support of a leftist SPOZ party, a small splinter group from the center-left Social Democratic party he used to lead.

Political analysts say their popularity is another reminder of the public's exasperation with the country's larger, mainstream parties, following a round of harsh austerity measures and sleaze scandals.

Czech presidents do not have the executive powers held by the leaders of France or the United States. But they wield significant influence over the cabinet and parliament through their ability to delay legislation and appoint prime ministers and other officials.

The office, held by anti-communist dissident and writer Vaclav Havel from 1990-2003, is held in high esteem in the country of 10.5 million people.

Senate speaker Milan Stech said an anticipated second round run-off between the top two candidates for the presidency would take place two weeks after the first round of the election.

(Reporting by Jan Lopatka; Editing by Andrew Heavens)