The talented goalkeeper has signed a contract with Spurs until June 2031 and will wear the number 31 shirt.
According to media reports, the London club will pay around £16.5 million for Kinsky, with another £2.5 million in bonuses.
Kinsky has carved out a position as a clear number one in the summer and played all 19 of Slavia's league games this season so far, conceding just seven goals. He also performed very well in the Europa League.
The talented goalkeeper had been a Slavia player since 2021 when he transferred from Dukla. Subsequently, he was first on loan in the second league Vyskov and then in Pardubice, who he helped to stay in the top competition.
He returned to Slavia last summer and his performances earned him an invitation to the national team in the autumn, but he has yet to start on the international stage.
Kinsky could immediately take over the number one role at Tottenham, as Italian goalkeeper Guglielmo Vicario, who started the season in that role and was a Spurs mainstay, broke his ankle and may not return in goal this season.
Vicario's replacement Fraser Forster is also suffering from health problems and hasn't been the most reliable in previous games.