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.”