Diouf has been attracting the attention of foreign clubs for a long time, with Crystal Palace reportedly keen in January, but failing to reach an agreement with Slavia.
The Senegal international now looks set for a move to the Premier League with West Ham in what could be the most expensive outgoing transfer from the Czech league.
"It's a very interesting offer, I think the most expensive departure in the history of the league," said Slavia's sporting director Bilek.
West Ham had been the main bidder for some time, but negotiations dragged on until the Hammers were greatly helped by the sale of Mohamed Kudus to Tottenham for £55m.
Slavia boss Jaroslav Tvrdík announced at a press conference on Friday that there had been no progress on the deal.
"We are patient. Either we will come to an agreement with West Ham or we will wait for offers from other clubs."
However, the manager also admitted that it was likely Diouf would leave.
"My personal guess is that he will be gone before the first round," he said in an interview with Livesport.
Tvrdik also hinted on social media on Sunday that it was a done deal. "Two in a year," he cryptically posted.
The manager was likely referring to the fact that Slavia managed to sell two players to the Premier League in one year - after goalkeeper Antonín Kinský left for Tottenham in the winter.
Sporting director Bilek has now confirmed the transfer will go ahead.
The Senegal international scored seven goals in 27 league games last season from defence, contributing significantly to winning the title and qualifying for the Champions League.