Klopp has been in charge of the Reds since October 2015 but is leaving at the end of the season after a reign that has seen him win the Premier League, Champions League, FA Cup and two EFL Cups.
After Klopp’s announcement in January several managers were considered leading contenders, but in April BBC Sport learned that Slot was set to get the job after a compensation deal worth up to £9.4m was agreed with Feyenoord.
“I can confirm that I will become the trainer there next year,” Slot said on Friday.
“Until now I was not thinking about this being the build-up to my last match, but that starts coming now. At the beginning of the week you are thinking about training and those kind of things.
“But the feeling gets stronger now. That is why I’m a little bit late now [for the news conference], because I wanted to say goodbye to some people personally and take time for them, more than just shaking hands.
“I understand that good results help, but it is very nice to feel that people really are thinking it’s a pity that I’m leaving.”
Slot’s final game at Feyenoord after three years in charge will be Sunday’s Eredivisie home match with Excelsior.
Klopp’s time at Liverpool ends on the same day with a home Premier League game against Wolves.
Feyenoord confirmed the 45-year-old’s departure on social media, saying: “The Arne Slot era is coming to an end. Let’s enjoy the last moments.”
Liverpool have not commented on the announcement.
Why have Liverpool chosen Slot?
Similar ethos should aid Arne Slot’s Liverpool transition, says David James
Slot led Feyenoord to the 2022-23 Eredivisie title, while this season they have won the Dutch Cup and are going to finish second in the league.
It is believed that the attacking style of Slot’s teams, his personality and his ability to develop players are key factors in making him Liverpool’s choice for the job.
Slot took over as Feyenoord manager in 2021 and confirmed his interest in managing in the Premier League when he was linked with Tottenham in 2023.
Former Liverpool midfielder Xabi Alonso, who guided Bayer Leverkusen to their first Bundesliga title this season, was linked with the position at Anfield.
But the 42-year-old Spaniard ended speculation in March when he said he would remain with Leverkusen.
Sporting Lisbon’s Ruben Amorim was also reported to have been a contender to take over from Klopp.
Slot’s route to Liverpool
The making of Arne Slot: The slow midfielder with the fastest brain
A former midfielder, Slot spent his entire playing career in the Netherlands, making well over 100 appearances for both FC Zwolle and NAC Breda in 18 years as a player.
After retiring from playing, he began his coaching career as a youth coach at PEC Zwolle before moving to SC Cambuur to become an assistant manager.
He moved to AZ Alkmaar in 2017 and stepped up to become manager two years later.
In his first season in charge, they were second, level on points with leaders Ajax, when the Covid-19 pandemic brought the season to a premature end. Nobody was awarded the title.
He was sacked in December 2020 when it emerged he had been negotiating with Feyenoord.
Slot took charge of Feyenoord in the summer of 2021 and won the Eredivisie with the club in 2022-23, losing only two league games, and won the Dutch Cup this season.
