However, in a departure from tradition, the Dutchman will become the club's first head coach rather than manager.
The PA news agency understands Slot has signed a three-year contract and will officially take over on June 1, subject to a work permit.
Liverpool's exhaustive search - incorporating sophisticated data analysis, character and performance research, market assessment, performance evaluation and various other indicators - identified the 45-year-old as their preferred candidate several weeks ago and his desire to take the job allowed for a swift appointment.
It has been an open secret for some time, with Liverpool paying Stg 9.4m compensation to Feyenoord, and Slot confirmed Anfield was his next destination on Friday.
Liverpool were keen to move swiftly to replace Klopp with a number of other top European clubs also looking to recruit managers in what was seen as a "challenging market" this summer.
Slot was attractive to owners Fenway Sports Group (FSG) as they believe he has demonstrated a reputation for over-performance with AZ Alkmaar and Feyenoord, being able to bring the best out of players and has a clear footballing identity, while also adopting an holistic and collegiate approach which fits with their ethos.
His job title of head coach means he fits into the new football structure which has had an overhaul in the last few months with two former sporting directors - Michael Edwards and Julian Ward - returning to the fold as FSG's chief executive of football and technical director respectively.
New sporting director Richard Hughes has been recruited from Bournemouth and will officially begin work on June 1.
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