The BBC is to pay £75,000 in libel damages to Harold Wilson's former secretary over her portrayal in drama-documentary The Lavender List.
Gina McKee played Lady Falkender, then Marcia Williams, in the drama
The BBC Four drama wrongly claimed Lady Falkender had an affair with Harold Wilson and exercised undue influence over his resignation honours list.
Wilson's honours caused a scandal for rewarding several businessmen who were felt to be against the Labour Party.
Lady Falkender said she was "glad that matters have been resolved".
In the out-of-court settlement, the BBC agreed to pay damages and legal costs, and said it would never re-broadcast the programme.
Rumours that Lady Falkender was the principal author of the honours list have circulated for years.
But she said in a statement: "A lot of nonsense has been written about the 1976 resignation honours list. My claim against the BBC has, I hope, given me an opportunity to nail the lie once and for all.
"As Lord Wilson always made clear throughout the period after he left office, and as I have myself always made clear, the 1976 list was his own work and included only those individuals he himself believed ought to be honoured.
"My involvement in the preparation of the list was no different to that of any other political secretary and the suggestion that I had means at my disposal of imposing my wishes upon Lord Wilson is simply untrue."
The drama depicted the last days of Harold Wilson's government
Responding to Lady Falkender's statement, the BBC said the programme "was not intended to establish historical fact".
"The Lavender List was a dramatisation of a particular perspective of Harold Wilson's last administration from 1974 to 1976 - a perspective challenged by Lady Falkender," it said in a statement.
"The BBC is not in a position to determine which factual perspective is accurate and has apologised for the upset and embarrassment caused to Lady Falkender."
The Lavender List was shown on BBC Four last March.
Written by Private Eye's deputy editor, Francis Wheen, it starred Gina McKee as Lady Falkender, who was known as Marcia Williams during her time in Downing Street.
The drama also featured Celia Imrie, Neil Dudgeon, and Kenneth Cranham as Harold Wilson.