The White House's National Security Adviser, Condoleezza Rice, will appear before the 9/11 commission on 8 April.
Ms Rice's appearance is seen as a major change of position
It follows the president's decision to drop his refusal to allow Ms Rice to testify on oath and in public.
The inquiry is looking at whether the 9/11 attacks could have been prevented, and Ms Rice is a key witness.
The Washington Post has published part of a speech on national security Ms Rice was to have given on 11 September 2001 which made no mention of al-Qaeda.
But documents released on Thursday show the president had ordered plans for military action against al-Qaeda.
A secret presidential directive dated 4 September 2001 told Defence Secretary Donald Rumsfeld to plan for military options "against Taleban targets in Afghanistan, including leadership, command-control, air and air defence, ground forces, and logistics".
However, while Ms Rice's aborted speech mentioned terrorism, it focused mainly on missile defence, with little discussion of the threats from Islamic extremist groups.
"We need to worry about the suitcase bomb, the car bomb and the vial of sarin released in the subway," it said, The Washington Post reported.
"[But] why put deadbolt locks on your doors and stock up on cans of mace and then decide to leave your windows open?"
Former White House counter-terrorism advisor Richard Clarke has testified to the commission that he gave several warnings to Ms Rice and her staff on the threat from al-Qaeda.
Ms Rice is considered a key witness for the commission, which is looking into policy against the terror threat before 11 September 2001, and the response afterwards.
The White House had said her public appearance would contravene the constitutional separation of powers.
The offer to drop that refusal was made on condition that it will not set a precedent.
President George W Bush said it would help give Americans "a complete picture" of events leading to the attacks on 11 September 2001.
The BBC's Justin Webb, in Washington, says the move was a U-turn of breathtaking proportions executed by a White House which is focused above all else on winning the president's re-election in November.
The commission head and relatives of the victims of the attacks had demanded that Ms Rice testify.
According to polls, the American public did not approve of what some saw as constitutional nitpicking over Ms Rice's testimony.