Schlumberger, who has joined from Bundesliga side Schalke, will augment the current staff in a new specialist position as head of recovery and performance.
The 54-year-old's role will sit between Andreas Kornmayer, the head of fitness and conditioning, and those of head of physio Lee Nobes and Dr Jim Moxon, the club doctor.
Klopp had wanted to bolster his backroom staff and, in Schlumberger, has recruited an expert used to the methods of the Reds boss having worked with him for three years at Dortmund. Schalke's ongoing financial problems meant they were open to the move, reports the Liverpool Echo.
Schlumberger had earlier worked with Nuremburg and the German national youth teams, and later moved to Bayern Munich and then Borussia Moenchengladbach.