Chvátal will also become Sazka CZ chairman, with Veselý moving up from his previous role as marking director.
That means Veselý will be in charge of Czech operations, while Chvátal continues running international affairs for the company.
The operator confirmed the change when contacted on the story by Gambling Insider.
Veselý is quoted as saying by Czech media: "Over the last eight years, we have managed to build a modern entertainment company from a traditional lottery company.
"Thanks to innovation and online transformation, we can offer a wide portfolio of games that appeals to three quarters of the adult population in the Czech Republic.
"My main goal is for Sazka not only to maintain the set trend but above all to further develop its long-term strategy of an entertainment company."