LONDON — The notices are flooding people’s inboxes en masse, from large technology companies, including Facebook and Uber, and even from parent teacher associations, children’s soccer clubs and yoga instructors. “Here is an update to our privacy policy,” they say.

All are acting because the European Union on Friday enacts the world’s toughest rules to protect people’s online data. And with the internet’s borderless nature, the regulations are set to have an outsize impact far beyond Europe.

In Silicon Valley, Google, Facebook and other tech companies have been working for months to comply with the new rules, known as the General Data Protection Regulation. The law, which lets people request their online data and restricts how businesses obtain and handle the information, has set off a panic among small businesses and local organizations that have an internet presence.

Brazil, Japan and South Korea are set to follow Europe’s lead, with some having already passed similar data protection laws. European officials are encouraging copycats by tying data protection to some trade deals and arguing that a unified global approach is the only way to crimp Silicon Valley’s power.

“We want to achieve the same level of restrictions that you have in Europe,” said Luiz Fernando Martins Castro, a lawyer based in São Paulo who advises the Brazilian government on internet policy. Mr. Castro said Europe was “pushing the matter and making people realize that we have to go forward.”

Europe is determined to cement its role as the world’s foremost tech watchdog — and the region is only getting started. Authorities in Brussels and in the European Union’s 28 member countries are also setting the bar for stricter enforcement of antitrust laws against tech behemoths and are paving the way for tougher tax policies on the companies.