The defence said the three were trying to help persecuted Muslims in war zones, providing relief and humanitarian aid.
The US government portrayed the arrest of Padilla, a US citizen, as an important victory in its "war on terrorism" and announced they suspected he was part of an al-Qaeda plot to detonate a radioactive "dirty bomb" in the US.
He was termed an enemy combatant and was interrogated about the plot in military custody, with no lawyer present, and was not read his constitutional rights against self-incrimination.
Subsequently, the charges brought against him in the civilian court in Miami did not include the "dirty bomb" allegation.
Federal case
His lawyers fought for years to get his case transferred into the federal courts.
Then in 2005, just as the US Supreme Court was about to consider the authority of George Bush, the US president, to keep Padilla detained, his case was sent to the federal court in Miami.
The key piece of physical evidence against Padilla, Hassoun and Jayyousi was a five-page form Padilla supposedly filled out in July 2000 to attend an al-Qaeda training camp in Afghanistan.
The form, recovered by the CIA in Afghanistan in 2001, contained seven of Padilla's fingerprints and several other personal identifiers, such as his birthdate and ability to speak Spanish, English and Arabic.
Also central to the investigation were some 300,000 FBI wiretap intercepts collected from 1993 to 2001, mainly involving Hassoun and Jayyousi.
Most of the conversations were in Arabic and purportedly in code.
The three are expected to be sentenced on December 5.