Edinburgh Rugby managing director Craig Docherty said the proposal was not "commercially compelling".
Saracens tackle Edinburgh at Murrayfield on Saturday in the opening Pool One fixture of this season's tournament.
But the Aviva Premiership club were keen to play the return fixture - scheduled for January 20 - in Cape Town.
Saracens have already taken one "home" Heineken Cup fixture abroad this season, opting to tackle French club Racing Metro at the King Baudouin Stadium in Brussels on Saturday week.
Moves to play a Heineken game against Biarritz in Cape Town, meanwhile, did not come to fruition last term.
Edinburgh reached last season's Heineken semi-finals, beating four-time tournament winners Toulouse on the way in a thrilling quarter-final at Murrayfield that attracted a crowd close to 40,000.
Docherty said: "As a club, our commitment is to our fans and other key stakeholders, such as sponsors, and fundamentally our goal is to qualify from what is a very challenging Heineken Cup pool.
"Following Edinburgh Rugby to South Africa is simply not an option for the vast majority whose support was so crucial to our journey to last season's semi-final.
"I am sure they will be desperate to support us in what could be a critical pool game.
"The case made by Saracens was not commercially compelling and, from a performance perspective, would have had a detrimental effect on our preparation for - and recovery from - this match.
"Edinburgh Rugby are open to new and innovative ideas, but the prospect of playing our final pool game in the southern hemisphere was simply not an option that we could seriously consider from a number of different perspectives.
"We consulted with tournament organisers ERC (European Rugby Cup) and Scottish Rugby throughout this process, and both are happy with our decision."
Saracens' official fixture list currently has the Edinburgh game down to be played at Vicarage Road in Watford.
It would be Saracens' last game there before moving to a new home - Allianz Park in Hendon.
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