The decision has come quietly, with no mention in The Sun itself, but a short story has appeared in its sister newspaper The Times, on page 3.
The Sun didn't have a topless model in Monday's edition, instead there was a photo of model and actress Rosie Huntington-Whiteley wearing lingerie. Today the third page of The Sun has a photo of two Hollyoaks actresses in bikinis.
The Times reported that the model on Friday 16 January would be the last to appear topless. A Sun spokesman was reported as saying, "Page 3 of The Sun is where it's always been, between pages 2 and 4, and you can find Lucy from Warwick at Page3.com."
A News UK spokesman said the news was "idle speculation by people who don't work on the newspaper", but the lack of a firm denial will has allowed a firm consensus that it looks like Page 3 is history to build online.
The feature has run continuously since 1970, when newspaper mogul Rupert Murdoch bought The Sun, then a struggling newspaper with a circulation of around 800,000, from IPC.
Murdoch transformed the newspaper, making it the best-selling daily in the UK.
The first Page 3 girl was the German model Stephanie Rahn, who appeared in November 1970 under the editorship of Larry Lamb. For many years the shots were taken by the photographer Beverley Goodway, who died in 2012.
The Sun will continue to show pictures of topless models on its Page3.com website.
Pressure groups have called for the end of topless models on Page 3 ever since the feature began. That pressure has increased in recent years.
The site Nomorepage3.org has won more than 217,000 signatures for its campaign, but at the time of writing had not updated the site with the news, although its Twitter account was abuzz with messages of congratulations from its many supporters, including the MPs Caroline Lucas and Sadiq Khan.