Assange has been seeking political asylum inside Ecuador's embassy in London since last week as he tries to avoid extradition to Sweden, where he is wanted for questioning about alleged sex offences.
A spokesman for the Metropolitan police service said: "The MPS have this morning, Thursday 28 June, served a surrender notice upon a 40-year-old man that requires him to attend a police station at date and time of our choosing. This is standard practice in extradition cases and is the first step in the removal process."
He said Assange remained in breach of his bail conditions, adding: "Failing to surrender would be a further breach of conditions and he is liable to arrest."
It is understood Assange has been ordered to present himself at Belgravia police station at 11.30am today.
On Sunday, Ecuador's ambassador to the UK left London to return home for talks on Assange's application for asylum.
Ecuador says Assange is under the country's protection while it considers the application. Assange, 40, faces arrest for breaching the terms of his bail if he leaves the embassy.
The Foreign Office confirmed in a statement that the Australian was "beyond the reach of the police" while he remains in the building.
Assange was set to be extradited to Sweden, where he faces accusations of raping a woman and sexually molesting and coercing another in Stockholm in August 2010 while on a visit to give a lecture.
Assange, whose WikiLeaks website published a mass of leaked diplomatic cables that embarrassed governments and international businesses, denies all charges, saying the sex was consensual and the allegations against him are politically motivated.
Earlier this week, a letter signed by leading US figures in support of Assange's application for political asylum in Ecuador was delivered to the country's London embassy. Among its signatories were Michael Moore, Oliver Stone, Noam Chomsky and Danny Glover. Others who put their names to it included the author Naomi Wolf, comedian Bill Maher and Daniel Ellsberg, the former US military analyst turned whistleblower, who leaked the Pentagon Papers in 1971 and has been a long-standing supporter of Assange.
Robert Naiman, policy director at the Just Foreign Policy campaign group, delivered the letter to the embassy on Monday, along with a petition signed by more than 4,000 Americans urging President Rafael Correa to approve Assange's request for asylum.
The letter, which has been posted online, states that its signatories believe Assange has good reason to fear extradition from the UK to Sweden, "as there is a strong likelihood that once in Sweden, he would be imprisoned, and then likely extradited to the United States".
Adding that the US government "has made clear its hostility to WikiLeaks", it says he could face the death penalty in the US if he was charged and found guilty under the Espionage Act.
"We also call on you to grant Mr Assange political asylum because the 'crime' that he has committed is that of practicing journalism," says the letter, which is addressed to Correa.
It concludes: "Because this is a clear case of an attack on press freedom and on the public's right to know important truths about US foreign policy, and because the threat to his health and wellbeing is serious, we urge you to grant Mr Assange political asylum."