Ahmad's family said they would be appealing against his extradition in the High Court.
The US alleges that Ahmad, 31, currently being held in jail in the UK, raised money to support terrorism in Chechnya and Afghanistan through internet sites and emails.
Ahmad, a computer expert from Tooting, south west London, has been accused of running websites inciting murder and urging Muslims to fight holy war.
He is currently being held in Woodhill Prison, Milton Keynes. In a posting on his website today, he said: "This decision should only come as a surprise to those who thought that there was still justice for Muslims in Britain.
"I entrust my affairs to Allah and His Words from the Quran."
It has taken Mr Clarke six months to decide on the case.
A judge ruled in May that Ahmad could be removed from Britain to face trial in the US, a decision which sparking anger among Muslim groups who branded it a "travesty of justice".
The Home Secretary had an initial 60 days to approve or reject the judge's decision.
But he was twice given two-month extensions because of the "complex representations made about the case".
The case could now come to the High Court on a judicial review application.
In previous extradition hearings in the case, Ahmad's lawyers complained he could be at risk of the death penalty if sent to the US and transferred to military jurisdiction at Guantanamo Bay.
A Home Office statement defended the time the decision had taken. It said: "As is right and proper, the Home Secretary has given full consideration to complex representations that have been made on Mr Ahmad's behalf but is satisfied that the conditions for his extradition have been met.
"It is a matter for Mr Ahmad as to whether he wishes to appeal this decision and the earlier decision of the District Judge that he is extraditable.
"The Government is fully committed to completing extradition cases relating to terrorist offences as quickly as possible."
A spokesman said strict time limits introduced in the Extradition Act 2003 were having "positive effects" and many cases were being resolved in six months or less.
A spokesman for Ahmad's family said: "This is a sad day for Britain and an even sadder day for British Muslims.
"In effect, this sends a message to British Muslims that there is no legal and democratic means to air your concerns. You must use other ways to get justice.
"We utilised every legal and democratic means to fight this decision.
"We held protests, wrote letters, lobbied MPs and compiled petitions of over 15,000 signatures, some even from as far away as New Zealand.
"But all of this amounted to nothing to the Government.
"If the floodgates for extradition are allowed to be opened, it will be British Muslims that will be targeted - the very people the British Government was hoping to win support from in the fight against terrorism."
Ahmad was arrested by British anti-terrorist police in August 2004 on an extradition warrant from the US, which alleged terrorist fundraising activities between 1998 and 2003, and he has been in jail since.
His case is, however, proceeding relatively quickly compared with some other extradition cases.
Britain's longest serving extradition prisoner is Rachid Ramda, who is wanted in France in connection with the 1995 Paris Metro bombing, and has now been in jail here for 10 years. There have been nine separate legal proceedings in the attempt to extradite the Algerian terror suspect across the Channel.
Also still in Belmarsh high security prison in south-east London is Abu Doha, the firebrand cleric wanted by the US in connection with the millennium plot to blow up an airport in Los Angeles. Doha was first arrested here in February 2001.
One of the functions of the Extradition Act 2003, which came into force on January 1, 2004, was to speed up the extradition process.
The new legislation came in after a working group made up of officials from the Home Office, Foreign Office and prosecuting authorities concluded that "a determined individual" had "an inordinate number of overlapping opportunities to challenge and delay their extradition".
Extradition proceedings were widely seen as too slow and cumbersome, allowing successive, multiple appeals to the High Court with further rights of appeal to the House of Lords.
The 2003 Act introduced procedures under which a wanted person has only a single right of appeal to the High Court with a further right of appeal to the House of Lords, if he gets leave.
Last week, Home Secretary Charles Clarke won crucial High Court backing for the new streamlined process. High Court approval for the changes was given in the case of a man wanted in Australia on cocaine smuggling charges.
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