The Sun newspaper will no longer feature topless women on Page Three, the Times has reported.
The Times, which has the same publisher as the Sun, said it understood Friday's edition of the Sun was the last that would carry images of topless women, although they would continue online.
Page Three has been a Sun feature for 44 years but has been criticised for being sexist and outdated.
The Sun's press office would neither confirm nor deny the reports.
Dylan Sharpe, the Sun's head of public relations tweeted on Monday: "Page 3 will be in the Sun tomorrow in the same place it's always been - between page 2 and page 4."
The Sun had already stopped carrying topless images at weekends, and sometimes did the same during the week.
Page Three of Monday's Sun featured model Rosie Huntington-Whiteley in lingerie, while Hollyoaks actresses Jennifer Metcalfe and Gemma Merna were photographed in bikinis on a beach on Tuesday.
The Times, which is a News UK title, said the paper had decided to quietly drop the feature.
It said it understood that News Corp executive chairman Rupert Murdoch had signed off the decision.
The topless images have long drawn protests from campaigners, with an online petition against their use attracting more than 215,000 signatures so far.
A campaign group called No More Page Three was founded in 2012 by Lucy-Anne Holmes, and has since gained support from a number of MPs and anti-sexism charities.
Ms Holmes told BBC Newsnight the group would not claim victory if scantily clad women continued to appear in the paper, but it was a "step in the right direction" if they were no longer topless.
She said: "The Sun hasn't suddenly decided that women say, think and do interesting and incredible things, it's still basically saying women are here for decoration."
'Matter for newspapers'
Downing Street said the prime minister believes it is up to newspapers to decide what they publish.
Number 10 declined to express any opinion over whether David Cameron welcomed the Sun's decision.
The prime minister's spokesman said: "He thinks what newspapers publish is a matter for newspapers. His view is that editorial decisions are for editors."
However, Education Secretary Nicky Morgan, who is also women and equalities minister, said the move was "long overdue".
She hailed it as a "a small but significant step towards improving media portrayal of women and girls", and added that she hoped it would be permanent.
Labour sources said Ed Miliband would be "pleased" by the decision as "he has said before it was out of date", according to BBC assistant political editor Norman Smith.
'Breasts not brains'
Labour MP Stella Creasy, also an anti-Page Three campaigner, told BBC Radio 4's Today programme: "The objectification of women in this way was basically saying to all of us that what mattered, frankly, were our breasts not our brains."
Media commentator Steve Hewlett argued the feature had been seen as "embarrassing" and its removal was evidence of the paper "trying to re-invent itself in the world post phone-hacking".
Jodie Marsh, who has appeared on Page Three a number of times, tweeted in defence of the Sun's feature: "So called 'feminists' really annoy me. Telling girls they shouldn't do page 3 is NOT being a feminist; women should do WHATEVER they want!!"
Former topless model Nicola McLean defended the feature to ITV, saying: "I don't think it is outdated.
"I think the girls still look fantastic on the page, they still clearly enjoy what they are doing, people still want to see it."
The Irish edition of the Sun stopped topless pictures two years ago.
Reports suggest the change to the paper edition may be reversed if it results in a noticeable drop in sales.