The two sides will now play two Tests and three one-day internationals, the dates and venues for which have yet to be announced, after the Board of Control for Cricket in India received assurances over the involvement of CSA chief executive Haroon Lorgat.
Lorgat is reported to have had a difficult relationship with all-powerful BCCI in his previous role as head of the International Cricket Council.
And the acrimony between the boards heightened further due to comments made by David Becker, a former legal advisor to CSA, earlier this month in which he accused the BCCI of flouting rules surrounding the Future Tours Programme.
In announcing the tour, CSA agreed to reduce Lorgat's role with the BCCI while the ICC are to investigate both his and Becker's conduct.
A joint statement from CSA and the BCCI read: "The agreement to tour was concluded by the two boards after various concerns were raised around the recent ICC Board meeting in London about the alleged conduct of CSA's Chief Executive,
Mr Haroon Lorgat, and recent comments made about the ICC Board by a former legal advisor to CSA, Mr David Becker.
"The ICC and CSA have already refuted the comments made by Mr Becker, and the ICC is now considering its legal options in respect of the same.
"In addition, the ICC will convene an investigation by an independent third party (to be appointed by the ICC) into the content and distribution of the media comments, subsequent attempts to have them withdrawn, and, in particular, the role of Mr Lorgat in relation to these matters.
"Pending the outcome of this investigation, CSA has ordered the withdrawal of Mr Lorgat from representing it at the ICC's Chief Executive's Committee (or from acting in any other ICC-related matters), and CSA has also withdrawn him from having involvement in any aspect of CSA's relationship with the BCCI, including but not limited to the upcoming tour.
"All parties have agreed that this investigation will be carried out in private, that no further media comment will be made until it has been concluded, and that its findings and recommendations will be binding upon CSA."
The shortened tour - the original schedule announced by CSA in July included three Tests, seven ODIs and two T20s - will result in a major financial hit for the South African board.The South African Cricketers' Association (SACA) expressed its disappointment at the truncated tour schedule.
"This is a huge blow not only to the players but also to the cricket loving public of South Africa," said SACA chief executive Tony Irish.
"Everyone is now deprived of a meaningful series, especially in the Test format between the world's top two cricket nations.
"I don't see how this can possibly be in the interests of either cricket in this country or of the global game. Cricket is the loser, plain and simple."
He added: "In addition CSA will suffer massive financial losses which will affect players, cricket programmes and cricket development at all levels in our country.
"It's a very sad day when international cricket becomes more about what happens off the field than what happens on it."