Arne Slot led Feyenoord to last season's Dutch title
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.
-- Courtesy of BBC Sport