The 74-year-old peace activist, who spent almost four months in captivity, flew from the Iraqi capital to Kuwait on a British military plane and will soon travel on to Britain.
Meanwhile Peggy Gish, a member of the Christian Peacemakers Teams organisation, said Canadians Harmeet Sooden, 33, and Jim Loney, 41, are preparing to depart Baghdad.
Ms Gish told a news conference in the Iraqi capital that the three men were "in good condition" and had not been tortured or abused by their captors.
The kidnappers however executed a fourth member of the group, US national Tom Fox, 54, whose body was found dumped in Baghdad two weeks ago.
The four peace activists were abducted on November 26 by a group calling itself the Brigades of the Swords of Righteousness, which threatened to kill the hostages unless all Iraqi prisoners were released.
Offering new details about the men’s ordeal, Ms Gish said for much of the time the men were not tied up. The kidnappers even gave Mr Kember medication for an illness, he is known to suffer from high blood pressure and an aneurysm.
Just before the raid that freed them on Friday morning, however, the three hostages were bound, according to Ms Gish.
"Then their captors left the building and so they were alone when the multinational forces came," she added.
The peace activists spent their first night of freedom at the British Embassy in Baghdad.
The rescue operation was put together in just three hours after US forces received information from two men they detained about the location of the house where the hostages were held.
The military declined to specify which forces took part in the mission, but officials in London and Ottawa said both British and Canadians were involved alongside US forces.