"I can confirm that I will become the trainer there next year," Slot told a news conference, according to ESPN.
Feyenoord confirmed Slot's departure, posting a video on X saying: "The Arne Slot era is coming to an end. Let's enjoy the last moments."
Liverpool have not yet confirmed Klopp's replacement, with the German manager leaving after the club's final game of the season against Wolverhampton Wanderers on Sunday.
Slot has been in charge of the Dutch club since 2021, and won the Eredivisie league title in 2022-23 along with the KNVB Cup this season. Feyenoord also reached the Europa Conference League final in his first season at the club.
Klopp announced in January that he would leave Liverpool at the end of this season. Although Bayer Leverkusen boss Xabi Alonso and Sporting Lisbon coach Ruben Amorim were previously linked with the job, Slot is set to take charge.
Slot had signed a contract extension with Feyenoord at the end of last season until 2026, with media reports saying Liverpool needed to pay the Dutch club an undisclosed sum for his signature.
