Liverpool said in a statement that the Dutchman, 45, would take up the position of head coach on June 1, subject to a work permit.
The club did not specify the length of his contract but it was widely reported in the British press that Slot had signed a three-year deal.
The new manager’s arrival was an open secret, with Liverpool reportedly agreeing a compensation deal worth up to £9.4 million ($12 million).
Slot confirmed Anfield was his next destination at his final pre-match press conference at the Eredivisie club on Friday.
Klopp, 56, announced in January that the 2023/24 season would be his last at Anfield, and took charge of his final game on Sunday, a 2-0 win against Wolves.
In his farewell speech to the crowd, Jurgen Klopp urged fans to throw their full support behind his successor, leading them in a chant of “Arne Slot, na na na na na”.
“You welcome the new manager like you welcomed me,” he said. “You go all-in from the first day. And you keep believing and you push the team.”
Slot, linked with a move to Tottenham last year, became Feyenoord boss in 2021 after impressing in his first managerial role at AZ Alkmaar.
He led the Dutch giants to the inaugural Europa Conference League final at the end of his first season, which they narrowly lost 1-0 to Jose Mourinho’s Roma.
Arne Slot then delivered just a second league title in 24 years to De Kuip last season before penning a new three-year deal.
“You can see people are genuinely sorry you are leaving,” he said on Friday.
“You can say that with words, but when you see it in people’s faces, it affects me quite a lot.”
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Feyenoord has enjoyed a strong season, winning the Dutch Cup and coming second to an all-conquering PSV Eindhoven side in the league.
Under Slot, Feyenoord has delighted the fans at De Kuip with an attacking brand of football and Slot has won praise from Klopp himself.
“I like the way his team plays football. If he is the one, I like that he wants it,” Klopp said last month.
“It’s the best job in the world, the best club in the world. Great job, great team, fantastic people. A really interesting job.”
Liverpool captain and fellow Dutchman Virgil van Dijk has hailed Slot’s attacking mindset, saying it would suit the philosophy at Anfield.
Speaking about the future under the new boss, Van Dijk said: “It is all about sticking together and giving him the chance of showing what he is capable of with the other guys who will come in.
“He probably knows already but everyone knows our expectations are always huge and it is about managing that in the right way and getting the maximum out of all of our players.”
Arne Slot has huge shoes to fill at Anfield after Jurgen Klopp restored Liverpool to the elite of English and European football during his nine-year reign.
Under his leadership, Liverpool won a sixth Champions League crown and a 19th league title, as well as a clutch of other silverware.
Initially, Bayer Leverkusen boss and former Liverpool midfielder Xabi Alonso was the favorite to succeed Klopp at Anfield.
However, Alonso committed to staying at Leverkusen as he led them to a first-ever Bundesliga title.
Liverpool finished third in the Premier League, qualifying for next season’s Champions League, and won the League Cup in Klopp’s final season.