The Senegal international joins from Rayo Vallecano on a five-year contract, with an option for a further year, in a deal Hull say surpasses the £20 million plus add-ons paid earlier this month for goalkeeper Konstantinos Tzolakis from Olympiacos.
The 21-year-old's arrival smashes a club transfer record that had stood since 2016, when Hull paid £13 million for Tottenham midfielder Ryan Mason.
"I am very happy to be here and very proud to be here as well," Mendy said. "I am a very athletic player, and I am a defender at heart.
"I also really enjoy the game and coming out from the back cleanly and aggressively when needed. I have wanted to play in the Premier League since I was little, so it's a great challenge to face and I am ready for it."
Mendy, who began his career at Paris FC before a route through Real Betis and Rayo Vallecano, scored twice in 28 appearances during his only season in La Liga, with his final outing coming in the Conference League final defeat by Crystal Palace in May.
It marked the second successive year he had reached that final, having lost with Real Betis against Chelsea the year before. His sole Senegal cap to date came against The Gambia in March.
Hull confirmed Mendy's arrival alongside that of 18-year-old Australia international Lucas Herrington, who joins from Colorado Rapids on a five-year deal for a fee reported at up to £13 million. Herrington made two appearances for Australia at this summer's World Cup, including a missed penalty in the last-32 shootout defeat by Egypt, and becomes the third most expensive player in Hull's history.
"The opportunity to play in the Premier League, one of the best leagues in the world, is a dream come true," Herrington said. "I've woken up at all hours in the morning in Australia to watch these games. To be a part of it is so special. I'm here to work hard and hopefully get a lot of games in the Premier League."
Hull City's business this week also extends to their existing squad, with the club closing in on a permanent deal to re-sign forward Joe Gelhardt from Leeds United following his season-long loan.
Gelhardt was a key figure in Hull's promotion campaign, scoring 14 league goals and adding another in the play-offs as Sergej Jakirovic's side beat Middlesbrough at Wembley to seal their return to the Premier League. Both clubs are working through the structure of a deal, with talks described as advanced and Hull keen to have the move finalised before their opening fixture of the new season.