The justices agreed to review a US appeals court ruling that Salim Ahmed Hamdan, a Yemeni accused of being Osama bin Laden's bodyguard and driver, could be tried by a military tribunal.
The high court will hear arguments in the case in the spring, with a decision expected by June. It will be the first time the court has decided a case involving the war on terrorism since rulings in June of 2004 that rejected the Bush administration's legal position.
The July 15 ruling by the appeals court was made by a three-judge panel that included Judge John Roberts, who was later nominated by Bush for the Supreme Court and who has become the chief justice.
Roberts said in the high court's brief order that he did not take part in considering Hamdan's appeal to the Supreme Court.
Roberts told the Senate Judiciary Committee that he would not take part on the Supreme Court in any matter in which he had participated while on the appeals court. The military tribunals, formally called military commissions, were authorised by Bush after the September 11, 2001, attacks.