Paranoid schizophrenic Haroon Aswat, from Dewsbury in West Yorkshire, admitted supporting terrorism and conspiracy and could face up to 20 years in prison.
Prosecutors say he and Hamza conspired to create a terrorist training camp in Bly, Oregon, 15 years ago.
Hamza, 56, previously of north London, was jailed for life in January after a jury last year found him guilty of supporting terrorist organisations.
Aswat, who is thought to be 40, was arrested in 2005 in Zambia and later flown to the UK.
He fought extradition for several years and was held at Broadmoor Hospital before being sent to the US last October.
The European Court of Human Rights in January dismissed a case he brought against the Government arguing that his extradition rested on inadequate assurances from US officials about his treatment.
His lawyers claimed that it had breached Article 3 (prohibition of inhuman or degrading treatment) of the European Convention on Human Rights.
In their ruling at the time, ECHR judges said the court found that it could not be said that there was a real risk that Mr Aswat would be subjected to treatment contrary to Article 3 if extradited.
Aswat’s lawyers told the court today that he has been treated for mental illness.
He will be sentenced on July 31.