The home secretary, who oversees law enforcement in the UK, will make the final decision on whether to extradite Assange.
“There is no reason why this court should not accept the assurances as meaning what they say,” the High Court ruling stated.
“There is no basis for assuming that the USA has not given the assurances in good faith.”
Assange’s fiancé, Stella Moris, called the decision a “grave miscarriage of justice” and said lawyers would file an appeal “at the earliest possible moment.”
Assange, 50, is currently being held at London’s high-security Belmarsh Prison. His supporters gathered outside the High Court on Friday, waving banners demanding his release.
A lower court judge earlier this year refused an American request to extradite Assange to the US to face spying charges over WikiLeaks’ publication of secret military documents a decade ago.
District Judge Vanessa Baraitser denied extradition on health grounds, saying Assange was likely to kill himself if held under harsh US prison conditions.
The United States appealed, challenging the notion that Assange’s mental health made him too vulnerable to withstand the US judicial system.
James Lewis, a lawyer for the US government, said Assange “has no history of serious and enduring mental illness” and does not meet the threshold of being so ill that he cannot resist harming himself.
The US has indicted Assange on 17 espionage charges and one charge of computer misuse over WikiLeaks’ publication of thousands of leaked military and diplomatic documents.
The charges carry a maximum sentence of 175 years in prison, although Lewis said “the longest sentence ever imposed for this offence is 63 months.”