The Czech team suffered two defeats and drew once at the group stage of the Euro 2016 before being eliminated from the tournament.
The result was a big disappointment for the Czech fans who had hoped for much more after the team won their qualification group which included last World Cup bronze medal winners, the Netherlands.
Vrba, 52, joined the national side in January 2014.
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Vrba had successfully managed top Czech league team Viktoria Plzen, winning two titles and bringing the club twice to the group stage of the Champions League.
The Czech takes over from Ruslan Agalarov, who resigned from his position last month.
Anzhi, which narrowly avoided relegation from the Russian top flight in the last season, did not say how long Vrba's contract was.
(Reporting by Robert Muller; additional reporting by Dmitriy Rogovitskiy in Moscow; editing by Amlan Chakraborty)
