The new law, set to come into effect on May 25, aims to give users more control over how their personal information is stored and used online, with big fines for firms that break the rules.
"New EU legislation means more data protection for you," the Silicon Valley giant said in the blue-and-white ad, which appeared in German dailies including Handelsblatt, Sueddeutsche Zeitung and the best-selling Bild.
It also appeared in Belgian newspapers, as well as in France's Journal du dimanche newspaper on Sunday.
Ahead of the introduction of the European Union's so-called General Data Protection Regulation, Facebook said it would be asking users to check their privacy settings and tell the firm how "we may use your data."
"You will also have the opportunity to access your data at any time, download it or delete it," the ad went on.
Facebook admitted earlier this month that up to 87 million users may have had their data hijacked by British consultancy Cambridge Analytica, which worked for US President Donald Trump during his 2016 campaign.
Facebook founder Mark Zuckerberg, who has repeatedly apologized for the massive data breach, last week told the US Congress that the more stringent EU rules could serve as a rough model globally.