Washington says Krekar, an Iraqi Kurd, is the founder of Ansar al-Islam, a group it alleges is linked to al-Qaida.
Krekar, whose real name is believed to be Fatah Najm al-Din Faraj, has lived in Norway as a refugee since 1991.
Washington suspects Krekar of involvement in the August 2003 bombing of the UN mission in Baghdad, and his name has also surfaced in the investigation into the 11 March train bombings in Madrid which killed 191 people and injured 1900.
One of the main suspects in the bombings reportedly met Krekar on several occasions.
National security threat?
Norway said last year it was revoking Krekar's refugee status because he had several times returned to Iraq.
Police earlier investigated Krekar for his possible involvement in the murders of Kurdish-Iraqi political rivals and the financing of terrorist activities, but the investigation was closed last June for lack of proof.
The Norwegian migrations department said the government "believes that he represents a threat to national security and has broken the conditions of his residence permit by returning several times to his country of origin".
In 2002, Krekar was held in custody in the Netherlands for several months and then in Norway on various charges.
He has repeatedly pleaded innocent to all accusations.
Krekar's lawyer said he would continue to appeal against his expulsion.