The Daily Mirror had alleged that the actor had behaved like a prima donna during the filming of the new series of the BBC's hit show 'Auf Wiedersehen Pet'.
Last month, Keith Chegwin accepted an apology from Trinity Mirror's Sunday tabloid The People after the television presenter brought libel proceedings against the paper over a story that claimed he tried to bribe a police officer. The paper apologised and agreed to pay a "substantial" sum in damages.
Laywers acting for Nail said that the article in the Daily Mirror, which was published last May, caused "grave damage" to the star's "personal and professional reputation". The damages being paid were not disclosed in court.
Keith Shilling, Nail's lawyer, said that had suffered "considerable embarrassment and distress" following the appearance of the piece.
Nail plays Oz in the award-winning series about a group of builders from the North East of England, which was first shown in the 1980s. The new series, which broadcast last year, reunited the characters in the US.
The article, headlined "Pampered Pet", included the allegation that during the filming of the new series of 'Auf Wiedersehen Pet', Nail behaved like an uncooperative prima donna and had upset the BBC and the rest of the cast.
Trinity Mirror's newspaper division MGN Ltd said it accepted that the allegations had "no foundation".
In a statement, Schilling said: "The defendant wishes today to publicly set the record straight and through its solicitor to personally apologise to the claimant for the distress and embarrassment it has caused him."
He added: "The defendant has also agreed to publish a prominent apology in the Daily Mirror and has agreed not to repeat the allegations and to pay a substantial sum by way of damages to the claimant, together with his legal costs."
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .