He is now wanted in London on the lesser charge of skipping bail and failing to surrender to a court.
The Metropolitan Police (MPS) statement came as it emerged that Sweden's director of public prosecutions, Marianne Ny, had decided to drop the rape investigation into the Wikileaks founder.
"Westminster Magistrates' Court issued a warrant for the arrest of Julian Assange following him failing to surrender to the court on the 29 June 2012. The Metropolitan Police Service is obliged to execute that warrant should he leave the embassy," the Met Police statement said.
"Whilst Mr Assange was wanted on a European Arrest Warrant (EAW) for an extremely serious offence, the MPS response reflected the serious nature of that crime. Now that the situation has changed and the Swedish authorities have discontinued their investigation into that matter, Mr Assange remains wanted for a much less serious offence," the statement said.
It said the MPS will provide a level of resourcing which is proportionate to that offence.
The Met declined to give details on its "operational plan" on Assange, who has lived in the Ecuadorean embassy in London since 2012, claiming that he fears being extradited to the US if sent to Sweden.
The 45-year-old could face trial in the US over the leaking hundreds of thousands of secret US military and diplomatic documents.
"Director of Public Prosecution, Marianne Ny, has today decided to discontinue the investigation regarding suspected rape (lesser degree) by Julian Assange," a brief statement from Stockholm said.
According to reports from Sweden, the Swedish prosecution hassaid that the decision to discontinue the investigation is not because they have been able to make a full assessment of the evidence, but because they don't see possibilities to advance the investigation.
"So we won't make any statements on the issue of guilt," the Swedish prosecution claims.
Assange reacted to the news by tweeting a photo of himself smiling inside the Ecuadorian Embassy, his home for the last five years.
"Focus now moves to UK," a Wikileaks spokesperson said.
In a report last year, the UN had called on Swedish and British authorities to free Assange from "arbitrary detention" in a report released last year and the UK had failed to overturn the findings on appeal.
Scotland Yard reportedly ran up costs of over 12 million pounds with 24/7 police security presence outside the Ecuadorian Embassy building, which was scaled back in 2015.
The Swedish investigation into alleged rape allegations against Assange has been dropped days after Chelsea Manning, who provided Wikileaks with classified intelligence on Iraq and Afghanistan that shocked the world, was freed from prison in the US.
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