Lauri Love, who has Asperger syndrome, is alleged to have stolen large amounts of data from the US Army, the Federal Reserve, the Department of Defence, NASA and the FBI in 2012 and 2013.
It is claimed that he placed hidden “shells” or “backdoors” within networks, causing “millions of dollars” worth of damage.
A Home Office spokesperson said: “On Monday 14 November, the Secretary of State, having carefully considered all relevant matters, signed an order for Lauri Love’s extradition to the United States.
“Mr Love has been charged with various computer hacking offences which include targeting US military and federal government agencies.”
In September, during a hearing at Westminster Magistrates’ Court, District Judge Nina Tempia ruled that Love could be extradited.
Following that ruling, Ms Rudd had two months to order the 31-year-old’s extradition.
If he is found guilty, his lawyers say he could be facing a sentence of up to 99 years in prison.
Love suffers from depression and eczema and has said that being imprisoned could lead to a mental breakdown or suicide.
Conservative MP David Burrowes, who has campaigned against his extradition, said Ms Rudd did not have much leeway to stop it happening.
Mr Burrowes, who represents Enfield Southgate, added that he expected Love to appeal.
“We hope that the High Court realises it would be disproportionate to extradite Mr Love and risk his life,” he said.
“Failing that, we have to rely on Donald Trump to step in and be our knight in shining armour.”
“President Obama is still going to be president until January, and we still hope that in one of his final acts he could stop the extradition.”
More than 100 MPs have signed a letter asking President Obama to block the extradition.
Labour MP Barry Sheerman, who is among them, said he was “deeply disappointed”.
“We are still keeping up the pressure. We are getting more and more MPs to sign the letter to President Obama,” he said.
“The pressure continues. We won’t give up.”
Love’s father, Reverend Alexander Love, said of the order: “It was going to happen – it was inevitable – but it’s still painful.
“I cannot begin to express how much sorrow it causes me. All we are asking for is British justice for a British citizen.”
Source: Sky News.