The Premiership club described Farrell's decision as a "surprise".
The former rugby league and rugby union England international was part of England's coaching team during this season's Six Nations Championship, but he opted to remain with Saracens after the tournament.
Speculation is now rife that Farrell will rejoin England's coaching staff.
Head coach Stuart Lancaster and his squad arrived in South Africaon Thursday for a three-Test tour highlighted by games against the Springboks in Durban, Johannesburg and Port Elizabeth.
Former England back Mike Catt has linked up with Lancaster and forwards specialist Graham Rowntree for the trip, although Farrell could now become involved again.
Saracens have announced that their former centre and long-serving player Kevin Sorrell would fill the role of backs coach with them.
Rugby director Mark McCall said: "Kevin is making a swift and successful transition from outstanding player to outstanding coach.
"He is Saracens through and through, and we are delighted he has agreed to take up this important post."
Regarding Farrell's exit, Saracens chairman Nigel Wray said: "We are sorry to see Andy leave, and we wish him well in the future."
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