Former international midfielder Bilek, who coached the Czech Republic between 2009 and 2013 and took them to the quarter-finals of the 2012 European championship, said he quickly agreed terms with the KFF.
"I flew to Kazakhstan on Monday and I returned to the Czech Republic on Tuesday," he said after signing a deal to take over from Feb 1.
The 53-year-old is the second Czech to coach Kazakhstan after Miroslav Beranek, who led the team between 2011 and 2013.
Bilek scored twice for Czechoslovakia at the 1990 World Cup and has coached several clubs at home as well as Slovakia, Georgia and Costa Rica.
Kazakhstan, who finished second in Group 1 in the fourth tier of the inaugural UEFA Nations League, have been drawn alongside Belgium, Russia, Scotland, Cyprus and San Marino in Group I of qualifying for Euro 2020.
"I understand that it will be difficult," said Bilek. "All rivals in the group are difficult. I think there’s no need to talk about Belgium. Russia also played very well at the World Cup."
The Central Asian country host Scotland in their first qualifier on March 21 and Russia three days later. Kazakhstan will meet Moldova in a friendly on Feb. 21 during their one-week training camp in Turkey.
Kazakhstan gained independence from the Soviet Union in 1991 and have never qualified for the World Cup or the European championship finals. (Reporting by Angel Krasimirov, editing by Nick Mulvenney)