Davies apologised for the "great damage and distress" his tweeting caused Lord McAlpine, Mr Justice Tugendhat heard.
Neither Lord McAlpine nor Davies was at the High Court in London for yesterday's hearing, where lawyers outlined details of the libel action to the judge. Davies's lawyer said the star hoped other Twitter users would be more aware of the "potential damaging consequences of tweeting".
In a statement issued after the hearing, Davies said he had apologised and made clear the allegations were false. He had also donated £13,000 to the NSPCC.
He added that after it emerged he was going to be sued for £200,000, he offered to pay £15,000 in damages plus a contribution to costs. "From my own experience, I am able to warn others of the dangers of re-tweeting," he added.
Davies's re-tweet concerned speculation about the identity of a political figure who was due to be the subject of a BBC Newsnight investigation.
Lord McAlpine's solicitor, Andrew Reid, said after the hearing: "Whilst Lord McAlpine accepts Mr Davies' apology concerning his tweet and subsequent re-tweet, the fact remains that both he and his family have been caused immeasurable distress which cannot be rectified."