The decision was hailed by critics who have campaigned against the sexist and offensive images.
According to insiders, the controversial feature would be removed from the print edition but would continue online.
'The Times', which is also owned by Murdoch, had reported that last Friday's edition of the paper would be the last to "carry an image of a glamour model with bare breasts on that page".
Instead, the pictures will now show scantily-clad women. In Monday's issue, the model Rosie Huntington-Whiteley was shown wearing Marks & Spencer underwear.
It "could be a huge step for challenging media sexism".
Topless Page 3 models were introduced by the tabloid in 1970, less than a year after media tycoon Murdoch bought the title.
Reportedly, the change may be reversed if it results in a noticeable drop in sales of the 'Sun'.
Publisher News UK has previously publicly argued that the feature remains popular with its readers and those who want rid of it do not buy the paper.
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