The statement confirmed an agreement had been reached among West Ham shareholders for Kretinsky to acquire shares which would increase his stake in the Championship club to 46 per cent.
Under the agreement, David Sullivan now holds 40 per cent as the second-largest shareholder in the Hammers, relegated from the Premier League last season.
A consortium featuring former Newcastle director Amanda Staveley had struck a deal to purchase the Gold family's 25 per cent stake in West Ham.
But that sparked a process allowing existing shareholders the opportunity to buy the Gold family's shares in the London club.
"I am deeply honoured to have the opportunity to become the largest shareholder of this great club," Kretinsky said.
"I appreciate the responsibility this brings and do not take it lightly. I would like to thank all continuing shareholders for their constructive efforts to enable this outcome and provide the club with the certainty it needs at this critical time.
"I look forward to communicating further with our supporters once the transactions are complete."
Vanessa Gold, representing the Gold family, said: "I am pleased that the West Ham shareholders have reached an agreement, with Daniel Kretinsky becoming the largest shareholder and taking a more active role in the decision-making at the club, as well as giving certainty to our fans and clarity over the future.
"My ambition through this process has been to ensure the club had the right leadership and to enable West Ham to achieve its potential and return to its rightful place in the Premier League."
Gold, whose late father David was a co-owner of West Ham alongside business partner Sullivan, added: "It has been an honour to serve the club as joint chair and director and to continue the legacy of my father David Gold.
"I will remain a small shareholder, but more importantly, I will forever be a passionate Hammers fan."
West Ham are currently 12th in the Championship, having won just one of their opening four league games.