"Today's decision forcefully repudiates the essential lawlessness of the Bush administration's failed Guantanamo policy," said Steven Shapiro of the American Civil Liberties Union.
The majority consisted of the court's four liberals - Justices John Paul Stevens, David Souter, Ruth Bader Ginsburg and Stephen Breyer, plus the moderate conservative Kennedy, who often casts the decisive vote.
The four conservative dissenters were Roberts and Justice Samuel Alito, both appointed by Bush, and Justices Scalia and Clarence Thomas.
The high court has ruled against the administration in two previous Guantanamo cases and in one other terrorism case.
Congress adopted new measures including the 2006 law aimed at keeping such cases out of court by stripping the prisoners of their habeas corpus rights under federal law.
The ruling marked the first time the court held that the Guantanamo prisoners have those rights under the U.S. Constitution.
Kennedy said the prisoners do not lose their right of habeas corpus review just because they are designated enemy combatants or because they are held at Guantanamo, which is outside U.S. territory.
The Guantanamo prison opened in January 2002 after the administration launched what Bush called a "war on terrorism" in response to the September 11 attacks.
"The entire basis for the existence of Guantanamo Bay is gone," said Navy Lt. Cmdr. Brian Mizer, a military lawyer assigned to defend Osama bin Laden's driver, Salim Hamdan, in the Guantanamo tribunals.
"It's a victory for all Americans because it reinforces the principle that no person or agency is above the law."
There now are about 270 prisoners at Guantanamo. Most have been held for years without being charged and many have complained of abuse.
Bush has acknowledged the prison's damage to the U.S. image and has said he would like to see it closed eventually. Both the Democratic presidential candidate Barack Obama and his Republican rival, Sen. John McCain, have pledged to close it.
McCain told reporters in Boston he was concerned about the decision. "These are unlawful combatants. They are not American citizens," he said. "But it is a decision the Supreme Court has made. Now we need to move forward."
Obama, while campaigning in Wisconsin, said in a statement the decision "is a rejection of the Bush administration's attempt to create a legal black hole at Guantanamo - yet another failed policy supported by John McCain."
The chief judge of the U.S. District Court in Washington, Royce Lamberth, said the court's judges would meet to consider how to proceed with the Guantanamo detainee cases in light of the ruling. There are nearly 200 Guantanamo cases before the court.
