Mr Assange has 14 days to appeal over the decision, the Home Office said.
It said the courts found extradition would not be “incompatible with his human rights” and that while in the US “he will be treated appropriately”.
Mr Assange is wanted by the American authorities over documents leaked in 2010 and 2011, which the US says broke the law and endangered lives.
The Wikileaks documents related to the Iraq and Afghanistan wars.
The Australian is being held at Belmarsh prison in London after mounting a lengthy battle to avoid being extradited.
Extradition allows one country to ask another to hand over a suspect to face trial.
Responding to the home secretary’s order, Wikileaks confirmed it would appeal against her decision.
Mr Assange’s wife, Stella, said her husband had done “nothing wrong” and “he has committed no crime”.
“He is a journalist and a publisher, and he is being punished for doing his job,” she said.
Media company Wikileaks is a whistle-blowing platform that publishes classified material provided by anonymous sources.