Vrba, 49, who guided unfancied Plzen into the Champions League in two of the past three seasons, replaces Michal Bilek who stepped down after a string of poor results scuppered the Czechs' World Cup chances.
"I'm very glad that we get a coach who has had many great results as well as recognition and support from professionals and the general public," said Miroslav Pelta, chairman of the Czech Football Association.
Vrba, a journeyman player during his career in the Czech league, will guide the Czechs as they seek to qualify for the 2016 European Championship. He is a popular choice among fans who had long criticised Bilek's cautious approach.
(Reporting by Michael Kahn, Editing by Clare Fallon)
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