He said Facebook could have done more to stop millions of users having their data exploited by political consultancy Cambridge Analytica in 2014.
"This was a breach of trust, and I am sorry," the back-page ads state.
It comes amid reports Facebook was warned its data protection policies were too weak back in 2011. The full-page apology featured in broadsheets and tabloids in the UK, appearing on the back page of the Sunday Telegraph, Sunday Times, Mail on Sunday, Observer, Sunday Mirror and Sunday Express.
In the US, it was seen by readers of the New York Times, Washington Post and Wall Street Journal.
In the advert, Mr Zuckerberg said a quiz developed by a university researcher had "leaked Facebook data of millions of people in 2014".
"I'm sorry we didn't do more at the time. We're now taking steps to make sure this doesn't happen again," the tech chief said.
It echoes comments Mr Zuckerberg made last week after reports of the leak prompted investigations in Europe and the US, and knocked billions of dollars of Facebook's market value.
Mr Zuckerberg repeated that Facebook had already changed its rules so no such breach could happen again.
"We're also investigating every single app that had access to large amounts of data before we fixed this. We expect there are others," he stated.
"And when we find them, we will ban them and tell everyone affected."
The ads contained no mention of the political consultancy accused of using the leaked data, Cambridge Analytica, which worked on US President Donald Trump's 2016 campaign.
The British firm has denied wrongdoing.