The bomber has been identified as Human Khalil Abu-Mulal al-Balawi.
He was picked up in a vehicle a small distance away from the CIA base in the Khost province of Afghanistan.
He was not thoroughly checked before being allowed to enter the highly secure base, media reports said.
Balawi's name for the first time was revealed by Al Zazeera, according to which he was a physician from the Jordanian town of Zarqa.
Incidentally, Zarqa is the home town of Abu Musa al-Zarqawi, the slain former leader of Al Qaeda in Iraq.
The Washington Post said Balawi had been working undercover in eastern Afghanistan for weeks, and had already provided US spies with what one official described as "actionable intelligence" when he set the trap.
A Jordanian intelligence official also died in the suicide attack.
Identified as Sharif Ali bin Zeid, the Jordanian intelligence officer was a member of the Jordanian royal family and was a first cousin of the king and grandnephew of the first king Abdullah, according to Jordanian press.
The New York Times said Balawi had been arrested in Jordan and recruited by its intelligence service — which believed that it had turned him into an ally — and then brought to Afghanistan to infiltrate the Al Qaeda organisation by posing as a foreign jihadi.
"He was definitely someone who could be seen as very helpful for something very important," an unnamed US official was quoted as saying.
"But the supposed intelligence asset was actually a double-agent who was given explosives by militants in the frontier region between Afghanistan and Pakistan, which he wore to a meeting last Wednesday at Forward Operating Base Chapman, the CIA base in the southeastern province of Khost," the daily said.
"The Jordanians believed that al-Balawi had been successfully reformed and brought over to the American and Jordanian side.
They set him up as an agent and sent him to Afghanistan and Pakistan to infiltrate al-Qaida," the NBC news reported.
"His specific mission, according to officials, was to find and meet Ayman al Zawahiri, al-Qaida's No 2, also a physician.
However, a Taliban spokesman, quoted on the Al-Jazeera Web site, said al-Balawi misled Jordanian and US intelligence services for a year.
The spokesman, Al-Hajj Ya'qub, promised to release a video confirming his account of the Afghanistan attack, the news channel said.
