Mohammed Saddiq Odeh, who is the second man charged by the United States authorities, allegedly told American agents that he was an active member of the Al-Qaeda group run by Osama bin Laden, who has declared an Islamic holy war against the US.
He reportedly said he had been staying with members of the group at the time of the embassy bombing. But he denied participating in the attack.
US officials said Mr Odeh accepted responsibility for the bombings because he was a follower of Al-Qaeda, which he believed conducted the attacks.
Mr Odeh has been charged with one count of murder for each of the 12 Americans killed by the explosion.
He also faces one charge of conspiring to carry out the bombing and one count of using weapons of mass destruction.
On Thursday, Mohamed Rashed Daoud al-Owhali, also known as Khalid Salim, was charged with the same offences.
Case against bin Laden
The Justice Department refuses to reveal details of the charges said to be in place against Mr bin Laden himself.
However, the BBC State Department correspondent in Washington, Richard Lister, says US officials believe the two men in American custody will help to build a convincing legal case against him.
Last week, the US carried out missile attacks against targets in Afghanistan and Sudan in retaliation for the embassy bombings.
Kenyans pass on suspects
Mr Odeh was arrested in Pakistan on the day of the embassy bombings.
He was said to have flown there from Nairobi using a fake passport and was en route to Afghanistan.
More than 250 people were killed by the Nairobi bomb which exploded almost simultaneously with another device outside the US embassy in Tanzania.
Only a small minority of those killed in Nairobi were American citizens. Most were Kenyans.
Our correspondent says Kenyan officials appear to have decided to avoid the possible risks involved in trying the two suspects there, although they still have the option to do so at some stage.