An official from the UK Home Office said London had now received the full request for extradition of the Australian.
The Washington Post reported that the US prosecutors had sent the request last Thursday before a legal deadline expired.
Assange is set to face a hearing in London over the extradition on 14 June.
He was later sentenced to 50 weeks in jail for skipping bail at the time he fled into the Ecuador embassy; at that time, he was wanted in Sweden for questioning on rape allegations made against him by two women. Sweden subsequently reopened the rape probe and sought his extradition; it had dropped the charge and cancelled the warrant in May 2017.
But a Swedish judge shot down the chances of his being extradited to that country, rejecting a request in early June to issue an arrest order.
Soon after his arrest in London, the US sought his extradition to face charges of computer hacking and being involved in a compromise of classified information, a charge that carries a maximum sentence of five years.
Washington revealed its hand on 24 May when it hit Assange with 17 new charges under the US Espionage Act over his alleged role in leaking documents from former US intelligence analyst Chelsea Manning in 2010.