Abu Hamza's solicitor, Muddassar Arani, says he will appeal against the home secretary's ratification of the extradition order. They have 14 days to do so.
Ms Arani, said: "There are grave concerns about what might happen if the extradition goes ahead.
"The Americans have said he will not face the death penalty or be sent to the Guantanamo Bay detention camp - but how can we be sure?
Torture fear
"I also fear that if he was sent to America he would become a victim of torture.
Ms Arani added: "I understand this might be a popular move with some sections of the public. But we have to ask ourselves whether it is morally right.
"We have standards in this country that will not be upheld if we extradite Abu Hamza and whatever people think of him they should understand that."
The US government wants to put Abu Hamza on trial on 11 charges.
It alleges that he funded terrorism, organised a "terrorist training camp" in Oregon between 1998 and 2000, and conspired to take 12 Westerners hostage in Yemen in 1998.
The American charges carry a potential jail sentence of 100 years. Abu Hamza's lawyers claim US evidence has been gained through torture.
Khalid Mahmood, MP for Birmingham Perry Bar, welcomed the home secretary's decision.
He said: "This sends out a clear message to preachers of hate - you are not welcome.
'Delighted'
"Those who propagate evil, hate and division cannot be a part of British society.
"This is excellent news for Britain's Muslim community. For too long Abu Hamza tarnished their name and now they will be delighted to learn he will face further charges in the US."
Abu Hamza was convicted in February 2006 of 11 of the 15 charges he faced in the UK.
He became well known as the imam of Finsbury Park mosque in north London but was dismissed from his position in 2003 after making speeches supporting al-Qaeda and criticising the invasion of Iraq.
