WASHINGTON — In a sweeping victory for privacy rights in the digital age, the Supreme Court on Wednesday unanimously ruled that the police need warrants to search the cellphones of people they arrest.

While the decision will offer protection to the 12 million people arrested every year, many for minor crimes, its impact will most likely be much broader. The ruling almost certainly also applies to searches of tablet and laptop computers, and its reasoning may apply to searches of homes and businesses and of information held by third parties like phone companies.

“This is a bold opinion,” said Orin S. Kerr, a law professor at George Washington University. “It is the first computer-search case, and it says we are in a new digital age. You can’t apply the old rules anymore.”

Chief Justice John G. Roberts Jr., writing for the court, was keenly alert to the central role that cellphones play in contemporary life. They are, he said, “such a pervasive and insistent part of daily life that the proverbial visitor from Mars might conclude they were an important feature of human anatomy.”

But he added that old principles required that their contents be protected from routine searches. One of the driving forces behind the American Revolution, Chief Justice Roberts wrote, was revulsion against “general warrants,” which “allowed British officers to rummage through homes in an unrestrained search for evidence of criminal activity.”

“The fact that technology now allows an individual to carry such information in his hand,” the chief justice also wrote, “does not make the information any less worthy of the protection for which the founders fought.”

The government has been on a surprising losing streak in cases involving the use of new technologies by the police. In Wednesday’s case and in a 2012 decision concerning GPS devices, the Supreme Court’s precedents had supported the government. “But the government got zero votes in those two cases,” Professor Kerr said.

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