Klimková oversaw 39 matches with the New Zealand women’s side since taking charge in 2021.
Of those 39 games, the Football Ferns won 11, with seven draws to go with 21 defeats.
She was at the helm for half of her six-year contract leading the team through a World Cup and Olympic cycle.
Klimková replaces national team coach Karel Radu, who resigned after his team were unsuccessful in their bid to qualify for the European Championships.
Football Association of the Czech Republic chairman Petr Fousek said: “She is the most successful Czech women’s football coach, who has many years of experience coaching at the highest level, especially in the USA, which is a powerhouse in women’s football.
“She has achieved a number of extraordinary successes abroad and it is good for us that she now wants to use her experience with the Czech national team.”
Klimková said: “I believe it is the right time to return and utilise my experience at home in the Czech Republic.
“Our main goal is to set a playing style that will contribute to success in the Nations League. Next year, we will then fight for participation in the Women’s World Cup.”