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Home Secretary Theresa May, who faced intense scrutiny during her efforts to deport Abu Hamza, said she was pleased that that the cleric "has finally faced justice" after using "every opportunity, over many years, to frustrate and delay the extradition process".
"His conviction was facilitated by this government's tireless work to successfully remove him from the UK to face trial in October 2012," she added.
A taped interview with a woman whose kidnapping was aided by Abu Hamza "stood out" in the imam's trial, a juror has said.
A recording of a conversation with the Egyptian-born preacher conducted by Mary Quin - a New Zealand national who was one of 16 tourists captured in Yemen in 1998 - was played to the court and "spoke in my mind significantly", Howard Baynson said.
In the tape, recorded during a visit to London's Finsbury Park mosque, the cleric told her "we never thought it would get that bad" - referring to the death of four of her travel companions.
The conviction of radical North London cleric Abu Hamza justifies the lengthy efforts made to extradite him from the UK, former home secretary David Blunkett said.
He said: "This has been a very long journey to obtain justice, and to ensure that someone who has been so adept at avoiding the just penalty for his extensive activities is at last being brought to book."
The 55-year-old preacher was jailed in the UK for seven years for soliciting to murder and inciting racial hatred in 2006 and first faced an extradition request from the Americans in 2004.
After a protracted legal battle he was extradited to the US in October 2012.
Abu Hamza is likely to appeal the verdict in his US terror trial, according to his defence lawyer, who cited "insurmountable" problems relating to the evidence presented in the process.
John Dratell told reporters outside the Manhattan court that his client believed his trial was "not about justice" but instead about "getting a conviction.
In a 1999 interview with ITV News' Alastair Stewart, Islamist cleric Abu Hamza claimed his radical followers were simply defending themselves.
He said Western democracies were the "aggressors" that were "blaming" Muslims for defending themselves.
The state prosecutor in Abu Hamza's trial has hailed the jury's unanimous guilty verdict, calling the Islamist cleric "not just a preacher of faith, but a trainer of terrorists".
Abu Hamza was convicted of 11 terror and kidnapping charges, including a charge that he helped kidnappers in Yemen in a 1998 attack that killed four people.
During the trial, he was accused of turning London's Finsbury Park mosque into an operations centre for the global export of violence and terror.
The Egyptian-born cleric was also found guilty of arranging for fighters to attend an Afghanistan al Qaida training camp.
Prosecutors said the defendant also financed and sent two men to Bly in Oregon to set up a compound to train others in terrorism.
Abu Hamza could face life imprisonment after being found guilty of all charges in his New York trial.
A jury of eight men and four women found the cleric, 56, guilty on all 11 counts he faced, handing Manhattan U.S. Attorney Preet Bharara his second high-profile terrorism conviction in three months.
The imam was extradited from the UK in 2012 after a series of court battles with the British government.
Islamist cleric Abu Hamza has been found guilty of all terror charges in his US trial.
Abu Hamza's US terror trial today heard that the Muslim preacher formerly worked for MI5 and co-managed a strip club in London's Soho.
Hamza's lawyer produced documents apparently from Scotland Yard that he said showed the radical cleric worked as an intermediary for the UK spy agency and had helped police defuse tensions with the Muslim community in Britain.
Hamza also told the New York court he had run a strip club in central London's party district after coming to the capital in the 1980s to "make money and enjoy myself", adding that some of the employment he gained was "on the wrong side of morality".
Hamza was extradited from the UK to America two years ago to face a string of terrorism charges, which he denies.