Egyptian-born Hamza, 56, was convicted after a trial in New York that a prosecutor said should provide justice for the victims of a kidnapping in Yemen more than a decade ago.
Hamza, who was tried under the name Mustafa Kamel Mustafa, was found guilty just weeks after an al-Qaida spokesman was convicted.
Hamza was accused of providing material support to terrorist organisations by enabling hostage-takers in the Yemen kidnapping to speak on a satellite phone, by sending men to establish an al-Qaida training camp in the US state of Oregon, and by sending at least one man to training camps in Afghanistan.
Following a lengthy legal battle, he was extradited in 2012 from the UK, where he led the Finsbury Park Mosque in the 1990s, reportedly attended by both September 11 conspirator Zacarias Moussaoui and shoe bomber Richard Reid. Hamza denied ever having met them.
Hamza looked straight ahead as the verdict was read out at the federal court. Sentencing was set for September 8, when he faces a maximum sentence of life in prison.
Defence attorney Joshua Dratel said the verdict was "not about the evidence but about a visceral reaction to the defendant".
US Attorney Preet Bharara said Hamza "attempted to portray himself as a preacher of faith but he was, instead, a trainer of terrorists".
For much of the past month, jurors watched videotapes and heard audio clips in which Hamza shouted to his followers, telling them non-Muslims could be treated like animals and women and children who were not Muslim could be taken captive.
But they saw a gentler version of Hamza on the witness stand, one who spoke confidently in the tone of a college professor as he insisted he never engaged in acts of terrorism or aided al-Qaida.
His testimony over four days was derided by Assistant US Attorney Ian McGinley, who told jurors to ignore his lies and concentrate on evidence.
In his closing argument, Mr McGinley read aloud the names of four European tourists who died in 1998 in Yemen after their convoy of cars was overtaken by extremist Islamic kidnappers, to whom Hamza had given a satellite phone. The prosecutor said a guilty verdict would provide a measure of justice for them and another dozen hostages who survived.
"Don't be fooled by his testimony," Mr McGinley said. "Don't let the passage of time diminish what he did."
Hamza also told jurors how he lost both hands, an eye and part of his forearms in a 1993 accident when he helped the Pakistani military as a civil engineer.