One of the men is said to be Usama bin Ladin’s finance chief.
The court said in a statement on Monday that Washington has provided guarantees that the men would not face trial in a military or special tribunal.
Germany is bound by its constitution not to extradite people to countries where they could face the death penalty.
The court began examining a US request for their extradition on 13 February amid complaints from Yemen that they should be returned there for questioning.
The final decision however, on whether to hand over the men – Muslim cleric Muhammad Ali Hassan Shaikh al-Moayad and his assistant Yahya Zayed, would be made by the German government, court spokesman Wolfgang Frank said.
Moayad and Zayed were arrested in Frankfurt on 10 January in an elaborate sting operation involving the US Federal Bureau of Investigation (FBI) and the German authorities.
They are suspected of having helped finance al-Qaida, but are not thought to have played a role in the 11 September, 2001 attacks in the United States blamed on the organisation.
Moayad’s lawyer said Thursday that he would appeal against the decision to Germany’s highest tribunal, the Constitutional Court in Karlsruhe.
He said that in making its decision, the Frankfurt court had relied almost exclusively on the evidence of a “dubious FBI informer”.
The FBI claims that Moayad, the imam of the main mosque in the Yemeni capital Sanaa, is bin Laden’s finance chief and had given the Saudi millionaire 20 million dollars.
German ZDF public television reported that he was suspected of links to the October 2000 attack on the warship USS Cole in Yemen which killed 17 crew and injured 38.
Zayed is thought to have provided logistical support for the organisation.
Germany has repeatedly refused Yemeni demands for the men to be returned because it says it has no official extradition treaty with Sanaa.
Moayad, who has reportedly been ill in prison, claims he was set up and lured to Germany after being told that a respected Muslim living in the United States wanted to donate money to charity in Yemen.
The imam is known in Yemen for his charity work, according to his supporters, and his arrest and subsequent detention sparked popular anger and has resulted in a number of protests.
Hundreds of suspected members of al-Qaida and remnants of Afghanistan’s former Taliban government are being held without formally being charged of any crime in a US navy base in Guantanamo Bay, Cuba.
Some are expected to be tried in military courts.
Moayad’s lawyer said he feared that his client might not be given a fair trial in the US.