The Press Association said that a compensation package for the 45-year-old, who had two years left on his contract, has now been agreed.
Slot had said Thursday that he was "confident" of landing the Anfield job.
Klopp will step down at the end of this season after a nine-year reign which brought the Champions League title in 2019 and Premier League trophy a year later.
"I like the way his team plays football. If he is the one, I like that he wants it," Klopp told reporters on Friday when asked to highlight Slot's qualities.
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