David Collier, chief executive of the ECB, had said Pietersen was "provoked" into sending the text messages which led to his exclusion from the England side this summer by South African players.
Those remarks reignited a long-running controversy which overshadowed the summer season but, with Pietersen back in the fold, the ECB is keen to move on.
Cricket South Africa and the South African Cricketers' Association had called for an apology following Collier's comments in a radio interview, in which he suggested they had used underhand tactics to unsettle Pietersen.
An ECB statement read: "CSA and ECB have discussed the events which led to Kevin Pietersen's non-selection for the third Test. Cricket South Africa has made clear to ECB that the electronic messages were not part of any initiative or plan to undermine the England team or players.
"ECB has unreservedly accepted that assurance and wishes to reiterate that it has no issue at all with CSA – or the Proteas players – on this matter and appreciates that the South African and England players follow the highest ethical standards of behaviour.
"Although the two boards do not agree on the sequence of events regarding any responses to messages between Kevin Pietersen and certain Proteas players, CSA and SACA accept Mr Collier's apology based upon his earlier utterances that the team may have acted in a way which was underhand.
"Both CSA and ECB regard this matter as now closed and will not comment on the confidential information shared in discussion between the boards."
Pietersen was dropped for the final Test between England and South Africa at Lord's in August and overlooked for the World Twenty20 following allegations he sent messages to Proteas players criticising his then captain Andrew Strauss.
After a stand-off period, Pietersen apologised for sending those messages earlier this month and signed a new ECB central contract after agreeing to enter a "reintegration" process with the team.
That might have been the end of the matter but for the Collier comments which infuriated the South Africans.
Collier said Pietersen's messages were replies to ones received from South African players – "a tactic which was used," he said.
Now an attempt has been made to finally draw a line under the controversy, even though there is disagreement with CSA over the sequence of events, the process of restoring Pietersen to the side will continue. Pietersen is due to start meeting senior players and management and could be added to the squad which travels to India later this month.