German prosecuters said Muhammad Ali Hasan Shaikh al-Muayad, imam of the main mosque in the Yemeni capital Sanaa, and Yahya Zayid were handed over to US authorities at Frankfurt airport on Sunday.
The pair were then flown to New York, they said.
Germany's highest court ruled on Thursday that their extradition could go ahead despite their entrapment in what was effectively a sting operation.
Muayad is suspected of being a finance chief for Usama bin Ladin's al-Qaida and Palestinian Islamic group Hamas, supplying both with weapons and communications equipment.
USS Cole attack
He also had been linked to the October 2000 attack on the USS Cole in Yemen which killed 17 crew and injured 38.
The men were arrested at Frankfurt airport in January.
They were said to have been enticed there by a Muslim working for the US Central Intelligence Agency who had studied at the same Quran school as Bin Ladin and Muayad.
It was that connection which allegedly persuaded Muayad to agree to take up to $25 million from an undercover agent to finance "terrorist" attacks.
Yemen is the ancestral home of
Usama bin Ladin
However, in an interview with a Yemeni newspaper, Muayad said he had been lured to Germany by a compatriot who wanted to invest in one of his charity projects in Yemen.
The authorities in Yemen repeatedly demanded that he should be given to them, but Berlin refused because it said it had no extradition treaty with Sanaa.
In its ruling, the constitutional court said the US had assured it that Muayad would not be brought before a military tribunal or put in a camp such as Guantanamo Bay and was likely to be given a fair trial.
Germany is bound by its constitution not to extradite people to countries where they could face the death penalty.
Muayad's lawyer said he would appeal the ruling to the International Court of Justice in the Hague if necessary.
Meanwhile, the Yemeni president has either freed or pardoned 146 men suspected of links with al-Qaida.
The official SABA news agency reported on Monday that Yemeni President Ali Abd Allah Salih had either freed or pardoned a total of 146 people suspected of links with al-Qaida, which carried out the 11 September 2001 attacks.
The official SABA news agency said on Monday that President Salih ordered the release of 92 Islamists after they swore not to attack non-Muslims or foreign embassies in Sanaa.
And a further 54 al-Qaida suspects who surrendered to the authorities had been pardoned by the president, SABA added.
"The security authorities will start from today to release 92 people accused of links to al-Qaida under orders from the president to free them in light of the results of a dialogue through the committee of ulemas or Islamic scholars," judge Hammud al-Hatar said.
Among the 54 who gave themselves up was Khalid Abd al-Nabi, an Islamist leader who heads the Aden-Abyan Islamic Army and the Islamic Jihad group.
Abd al-Nabi recently hosted a dinner for security chiefs who had cracked down on his gunmen in Abyan province in June.
The Yemeni interior ministry announced in June that security forces had killed six "extremists" and arrested 11 others in Jabal Hatat, 120km northwest of Aden.
Yemen was pressed to pursue
al-Qaida suspects after 9/11
A police official said Abd al-Nabi, 35, was one of the six killed.
But authorities said last month that the charred body turned out to be that of a Saudi and that Abd al-Nabi had surrendered.
Hatar, who heads the committee of ulemas set up a year ago to dialogue with opposition Islamists, said the releases and pardons "crown the policy of the president to settle ideological problems through dialogue".
Yemen, the ancestral homeland of Usama bin Ladin, has been under pressure from Washington since the September 11 attacks to crack down on presumed al-Qaida activists.
In a September 2003 report, rights group Amnesty International called on Yemen and the US to stop committing human rights violations in the name of security and "fighting terrorism".
Amnesty said security forces in Yemen embarked on mass arbitrary arrests, detentions and deportations of foreign nationals in the immediate aftermath of the September 11 attacks.
The arrests were carried out without judicial supervision and those detained were invariably subjected to lengthy incommunicado detention and interrogation.
During the interrogations some claimed they were tortured or ill-treated.