The decision that was welcomed by international news organisations reportedly came in response to an appeal against the ban filed by Aljazeera satellite TV and Reuters news agency.
The Associated Press had filed a similar appeal on behalf of a staffer denied accreditation, but hearings on it had not begun.
The court criticised the measure in place for nearly 30 months as "unjust and discriminatory" as well as damaging to Israel's image as a country which respects the freedom of the media.
Citing security concerns, Israel's government press office stopped issuing or renewing the official state press cards to Palestinian journalists about a year after the 2000 outbreak of the Palestinian Intifada (uprising).
The card is needed for access to Israeli government buildings, is also essential for passing through the many Israeli roadblocks in the West Bank and Gaza and for working as journalists in Israel-controlled parts of those territories.
Without the cards, Palestinian journalists, many of whom work for foreign news organisations, are largely stranded in their home towns and subject to obstruction by Israeli security personnel.
Denial still possible
The Foreign Press Association in Israel, which has long been at loggerheads with the press office on the issue, welcomed Sunday's court ruling and called for prompt implementation.
"This policy, in effect for some two and a half years, was unjust and discriminatory, badly hampered the media's ability to cover the news and grievously injured Israel's standing as a country that respects the freedom of the press," the FPA said.
Aljazeera and the Reuters news
agency challenged the ban
In their ruling, the three-judge panel of the Supreme Court said individual applications by Palestinian journalists could still be denied to applicants who lack permits to work in Israel or who fail a security check.
But it said a balance had to be struck between security concerns and the need for free and independent reporting, the rule of law and democracy.
"This is not just an interest of the journalists," they wrote. "This is in the general public interest."
Defending the ban, the government had argued that it feared the press cards and the access they grant, could be used improperly.
"The state argues that the refusal is due to fears of an attack on Israeli officials, at press conferences or in their offices," a court transcript said. But Sunday's ruling said the danger was "weak and theoretical".
"This policy, in effect for some two and a half years, was unjust and discriminatory, badly hampered the media's ability to cover the news and grievously injured Israel's standing as a country that respects the freedom of the press"
Israeli Foreign Press Agency
Since Palestinian applicants are still subject to security checks and other restrictions, it was unclear how many Palestinian journalists will benefit from the ruling.
"I really don't know," Daniel Seaman, director of the government press office said.
"We have to study the ruling and its implications. Those who meet the criteria will be issued cards. We shall honour the court's ruling."
The government press office has had rocky relations with local and foreign journalists in recent years. Last year, the government suspended plans that would have required stringent security checks for journalists to receive accreditation after an uproar by local and foreign journalists.