The Ukrainian three-times undisputed champion holds the IBF, WBA and WBC titles after vacating the WBO belt.
The 39-year-old has not boxed since beating Britain's Daniel Dubois at London's Wembley Stadium last July.
"I respect his (Verhoeven's) journey - he's truly the 'King of Kickboxing'. But this is boxing - a different game, with its own rules and its own kings," said Usyk, who has a 24-0 record.
"I'm ready and looking forward to meeting him in the ring. It's going to be a unique experience for both of us, and I know the fans are excited too. A big night is coming."
The 'Glory in Giza' fight will be streamed live on DAZN.
"I spent 12 years as the undisputed heavyweight kickboxing champion and accomplished everything I set out to accomplish," Verhoeven, 36, told The Ring.
"But staying at the top for that long didn't take away from the hunger, it strengthened it. Usyk is the undisputed in boxing. That's the kind of challenge that motivated me. Undisputed versus undisputed."
Verhoeven has sparred in the past with former champion Tyson Fury and had one professional bout in 2014, which he won by a knockout.
The Dutchman announced his departure from kickboxing last November after 76 fights and 66 wins.
Fury, who has his own comeback fight in April, and fellow Briton and former champion Anthony Joshua have also been involved in 'crossover' fights in the past, with both fighting UFC heavyweight champion Francis Ngannou.
WBO champion Fabio Wardley, who was handed the title when Usyk relinquished the belt and will seek to defend it against Dubois on May 9 in Manchester, was disappointed by the news.
"I don't feel like it's a real, genuine challenge nor someone that deserves the shot," the Briton told Sky Sports television.
"But I do understand or do concede Usyk is at a point in his career ... where he's able to do what he wants for a bit in that sense. He's earned the position to ... take an easy fight."