Babar Ahmad will appeal against his extradition to the US to face terror charges, say his family.
Lawyers say Babar Ahmad, in green, risks the death penalty in the US
Mr Ahmad, 31, a computer expert from Tooting, south London, is accused of running websites supporting terror and of urging Muslims to fight a holy war.
His wife Maryam said her husband would be appealing in the High Court.
Charles Clarke ordered his extradition after giving "full consideration" to representations made on behalf of UK-born Mr Ahmad, the Home Office said.
But Mrs Ahmad said he would be appealing both against the home secretary's decision and the original decision in favour of extradition made by a District Court judge in May.
She told BBC News 24 her husband should be tried in Britain, if at all.
"If the Americans were to provide the evidence and if he was to have a trial in this country it would be very easy for us to mount a defence in support of Babar to show that he isn't the individual they are pointing him out to be," she said.
"We've seen where the Americans have put forward allegations against an individual and eventually when it's come to court the case has been thrown out."
Mr Ahmad is being held in Woodhill Prison, Milton Keynes.
On a posting on his website 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."
The Muslim Council of Britain said it was "very disappointed" in the extradition ruling and feared it could contribute to "further alienation" among Muslim youths.
It questioned the fairness of the Extradition Treaty 2003 under which the US government does not have to prove to the UK that there is a prima facie case to answer.
"If our government has any evidence of wrongdoing on the part of Babar Ahmad then he should be charged in this country and put on trial here," spokesman Inayat Bunglawala said.
But the Home Office said: "The government is fully committed to completing extradition cases relating to terrorist offences as quickly as possible."
A spokesperson said the "positive effects of strict time limits" under the act had already been seen.
"Furthermore, we have begun a consultation on how it may be possible to expedite future extradition cases involving terrorism."
Meanwhile, a spokesman for Mr Ahmad's family said: "In effect, this sends a message to British Muslims that there is no legal and democratic means to air your concerns."
"We held protests, wrote letters, lobbied MPs and compiled petitions of over 15,000 signatures...
"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."
In May, District Judge Timothy Workman, sitting at Bow Street magistrates' court, ruled Mr Ahmad could be extradited, and the case was sent to the home secretary for final approval.
A Home Office spokesman said: "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."
In claims dating back to 1997, the US government has accused Mr Ahmad of "conspiring to support terrorism", saying he "sought, invited and solicited contributions" via websites and e-mails.
The US Department of State has claimed that websites run by Mr Ahmad urged Muslims to use "every means at their disposal" to train for jihad, or holy war.
The websites are said to call for support for terrorist causes in Afghanistan and Chechnya, as well as encouraging the transfer of money and useful equipment via the sites.
It is also alleged Mr Ahmad tried to set up a terrorist training camp in Arizona.
His lawyers have said Mr Ahmad would be at risk of the death penalty if he was sent to the US and transferred to military jurisdiction.