Julian Assange still faces the more serious allegation of rape.
However, Swedish prosecutors have run out of time to investigate Julian Assange for assault because they have not succeeded in questioning him.
The Australian journalist and activist denies all allegations and has said they are part of a smear campaign.
Julian Assange sought asylum in the Ecuadorian embassy in London in 2012 to avoid extradition to Sweden.
Under Swedish law, charges cannot be laid without interviewing the suspect.
Prosecutors had until August 13 to question Julian Assange about one accusation of molestation and one of unlawful coercion, while the time limit on a further allegation of molestation runs out on August 18.
The more serious allegation of rape is not due to expire until 2020.
An official announcement from the prosecutor’s office is expected on Thursday morning.
Julian Assange has always denied all the accusations and says he fled into the Ecuadorian embassy because he fears being extradited from Sweden to the US and put on trial for releasing secret American documents.
He has said in the past that he will not leave the embassy, even if the accusations of se* crimes are dropped.
The woman who accused Julian Assange of molestation and unlawful coercion – who is identified in legal papers only as AA – is said to be relieved that the case is now behind her.
Swedish prosecutors had initially insisted that Julian Assange be questioned in Sweden, but earlier this year – under pressure to advance the investigation – agreed that he could be interviewed in London.
The Swedish government has been unable to negotiate access with the Ecuadorian authorities, with both sides blaming the other for the impasse.
Lawyers for Julian Assange say the allegations of assault should have been dropped long ago.
He said he believed Julian Assange could clear his name over the rape allegation.
Sweden is expected to continue discussions with Ecuador over the terms under which the prosecutor could question Julian Assange over the remaining accusation.
The UK government has urged Ecuador to co-operate, stressing that the UK has a legal obligation to extradite Julian Assange.
The cost of policing the Ecuadorian embassy in Knightsbridge for the past three years now stands at around £12 million ($18.8 million).
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