The club did not specify the length of his contract in their statement but Sky Sports said it understood Slot had signed a three-year deal.
Slot’s arrival has been an open secret, with Liverpool reportedly agreeing a compensation deal worth up to £9.4 million ($12 million).
He confirmed Anfield was his next destination at his final pre-match press conference at the Eredivisie club on Friday.
Klopp announced his departure in January and took charge of his final game on Sunday, a 2-0 win against Wolves.
In his final speech to the Anfield crowd, the German urged fans to throw their full support behind Slot.
“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 moved to Feyenoord 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. They narrowly lost 1-0 to Jose Mourinho’s Roma.
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.”
Feyenoord have enjoyed a strong season, winning the Dutch Cup and coming second to an all-conquering PSV Eindhoven side.
Liverpool captain and fellow Dutchman Virgil van Dijk has hailed Slot’s attacking mindset, saying it would suit the philosophy at Anfield.
Initially, Bayer Leverkusen boss and former Liverpool midfielder Xabi Alonso was the favourite to succeed Klopp at Anfield.
However, Alonso has committed to staying at Leverkusen after leading them to a first-ever Bundesliga title.
Liverpool won the League Cup in Klopp’s final season in charge and finished third in the Premier League, qualifying for next season’s Champions League.
© Agence France-Presse
Photo: Twitter @AnfieldSector