The South African Rugby Union (SARU) cited factors including travel restrictions, player welfare, safety concerns and the ongoing effect of the coronavirus pandemic for pulling out.
The Springboks' absence leaves Australia, New Zealand and Argentina to challenge for this year's title.
It is a blow ahead of the tournament, and means the Tri-Nations returns eight years after Argentina joined to extend the competition to a four-team event.
SARU chief executive Jurie Roux said: "SANZAAR [the competition organisers] and Rugby Australia have bent over backwards to make the tournament happen and it would have been unfair on them and their partners and state government to delay a decision any longer.
"This is a hugely disappointing outcome for supporters and commercial partners but the ongoing impacts of the pandemic in multiple dispensations mean we are unable to deliver a Springbok team without seriously compromising player welfare, apart from other logistical challenges."
With a Tri-Nations return, six international matches will be played in Australia across six consecutive weekends.
The Tri-Nations will see each nation play each other twice, with games to be held in Sydney, Brisbane and Newcastle – starting on 31 October between the Wallabies and All Blacks at ANZ Stadium.
The first two matches involving Australia and New Zealand double up as the final two Bledisloe Cup matches.
SANZAAR chief executive Andy Marinos said: “COVID is just a gift that keeps on giving! Naturally, it is extremely disappointing that the Springboks, due to the continued complexities of operating in and around this COVID environment, cannot fully compete in the previously planned six-round Rugby Championship.
“That said, this now presents us with a unique opportunity, in this our 25th year, to close off 2020 with a Tri-Nations competition."