The court said it refused because the case “didn’t raise an arguable point of law.”
The decision likely exhausts Assange's efforts to avoid a trial in the US related to charges related to WikiLeaks' publication of classified documents more than a decade ago.
WikiLeaks wrote in a statement on Twitter that the case would now move to home secretary Priti Patel to authorise the extradition. They added that he's facing a 175-year sentence in the United States.
Assange could still seek to take his case to the European Court of Human Rights.