Publicist Max Clifford has paid damages to settle slander and libel proceedings brought by Neil and Christine Hamilton.
The Hamiltons are expected to be paid court costs and compensation
The case relates to comments made by Mr Clifford in 2001 while representing Nadine Milroy-Sloan, who falsely said the couple had sexually attacked her.
He agreed to pay an undisclosed amount - reported to be about £100,000 - to the Tory ex-minister and his wife.
Milroy-Sloan was jailed for three years in 2003 after being found guilty of perverting the course of justice.
Neil and Christine Hamilton brought 24 defamation claims against Mr Clifford over remarks made by him to newspapers and another one for comments he made during a live GMTV broadcast.
The publicist's decision to settle follows a pre-trial hearing at the High Court, in which Mr Justice Eady ruled out parts of his defence to the Hamilton's case against him.
Mr Clifford appealed against that decision, but later decided to settle.
In an agreed statement, read by the Hamiltons' solicitor Howard Pinkerfield, Mr Clifford says his remarks could have been taken to mean the sexual assault allegations were true but adds: "It was never my intention to suggest this as I had no direct knowledge whatsoever of the alleged events."
The statement continues: "I now accept and wish to publicly make it clear that there was no truth whatsoever in the allegations made by Nadine Milroy Sloan and I wish to entirely withdraw, without any qualification, all my remarks and comments which could be taken to mean otherwise."
Former MP Neil Hamilton said: "This has been a distressing period for both Christine and me and, having at last been utterly vindicated, we now wish to put this episode behind us."