He said he had been told the Russians possessed "dirt" on Hillary Clinton.
Separately, former Trump campaign manager Paul Manafort pleaded not guilty to charges of money laundering unrelated to the 2016 election.
The charges against Mr Papadopoulos are the first to be brought by Robert Mueller, the special counsel investigating alleged links between Russia and the Trump campaign.
How does the Papadopoulos case affect Trump?
It has the potential to damage the US leader because it relates directly to his campaign, analysts say.
Mr Papadopoulos - a Chicago-based international energy lawyer - was close enough to then-candidate Trump to be part of a photograph (third from left) of his national security team which Mr Trump tweeted on 1 April 2016.
According to the court documents, Mr Trump's former foreign policy adviser admitted on 5 October 2017 to having impeded the FBI's investigation into alleged collusion with Russia.
When he was interviewed by the FBI this January, he falsely claimed that he had met two figures with Russian connections before joining the Trump campaign in March 2016. In fact, he met them after joining the campaign.
One was an unnamed Russian woman who, Mr Papadopoulos believed, had connections to Russian government officials.
He admitted seeking to use her connections in an effort to arrange a meeting "between the campaign and Russian government officials".
The other person was an unnamed, London-based professor who was said to have "substantial connections to Russian government officials".
The professor only took an interest in Mr Papadopoulos because of his status within the Trump campaign, the statement says.
Russian "dirt" on Mrs Clinton, in the form of "thousands of emails", was allegedly mentioned by the professor at a breakfast meeting in a London hotel on or around 26 April 2016.
The professor said he had been informed about the compromising emails when he met senior Russian government officials on a recent trip to Moscow.
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