A former foreign policy adviser for the Trump campaign pleaded guilty to making false statements to FBI agents as they questioned him about his attempts to arrange meetings between members of the campaign and the Russian government, according to a criminal complaint unsealed Monday.

George Papadopoulos’s guilty plea was unsealed Monday after Robert Mueller’s special counsel team announced indictments against two other figures in the Trump campaign — former campaign chairman Paul Manafort and his former associate, Richard Gates.

Mr. Manafort and Mr. Gates pleaded not guilty Monday at the U.S. District Court in Washington, D.C.

According to the charges, which were originally filed in July, Mr. Papadopoulos made false statements to the FBI about his interactions and relationships with Russian officials when he was interviewed in January.

Court documents said Mr. Papadopoulos was fully cooperating with the special counsel, which resulted in prosecutors dropping an obstruction of justice charge and forgoing other charges they may have brought against him.

“Since his arrest, defendant has made efforts to cooperate with Special Counsel’s investigation by participating in multiple proffer sessions and voluntarily turning over materials at the request of investigators,” his lawyers said in a document filed under seal in early October, and made public Monday.

Christopher Swift, a white-collar criminal defense lawyer who specializes on Russia sections issues, said the guilty plea by Mr. Papadopoulos should alarm the White House.

“It shows that he has turned. If he had a good argument, he wouldn’t plead guilty,” he said. “It’s a tough spot to be in.”

Mr. Swift noted that the charge against Mr. Papadopoulos was relatively light but still could carry jail time, which is enough incentive to give Mr. Mueller “whatever information he has to try to mitigate his sentencing.”

“It gives Special Counsel Mueller leverage to get people higher in the food chain,” he said.

The government said Mr. Papadopoulos was in contact with a professor who had connections to Russian government officials and claimed to have “dirt” on presidential candidate Hillary Clinton in the form of “thousands of emails.” Mr. Papadopoulos told agents that he had learned this information before he became a part of Mr. Trump’s campaign, but in reality investigators said he met with the professor after he became a campaign advisor in March 2016 and the professor provided that information a month later.

At a March 31, 2016, national security meeting with then-candidate Donald Trump and other foreign policy advisers to his campaign, Mr. Papadopoulos told the group that he had connections that could help arrange a meeting between Mr. Trump and Mr. Putin.

The complaint states that in April 2016, the professor put him in contact with an an unnamed person who had connections to the Russian Ministry of Foreign Affairs as well as an unnamed Russian woman with whom he discussed arranging meetings between the Trump campaign and Russian government officials. The Russian woman was initially introduced to Mr. Papadopoulos as Vladimir Putin’s niece, but she was not in fact related to the Russian president.

Mr. Papadopoulos, 30, was part of the Trump campaign’s foreign policy team that was run by Jeff Sessions, who currently serves as attorney general, and included retired Army Lt. Gen. Keith Kellogg and consultant Carter Page.

He joined the Trump campaign after serving as an economic policy adviser for Ben Carson’s presidential run. Mr. Carson, a retired pediatric neurosurgeon who lost the Republican nomination to Mr. Trump, currently serves as the secretary of health and human services.

Court documents in Mr. Papadopoulos‘ case say he repeatedly wrote to campaign supervisors and an unnamed “high-ranking campaign official” to keep them apprised of his efforts and government officials’ interest in hosting Mr. Trump on a visit to Russia. None of the documents name any Trump campaign officials that he was in contact with. At one point, one of the campaign officials forwarded one of Mr. Papadopoulos‘ emails to another campaign member and indicated they were not interested in pursuing the meetings in Russia.

“We need someone to communicate that DT is not doing these trips. It should be someone low level in the campaign so as not to send any signal,” the campaign official wrote.

The lack of interest doesn’t appear to have been passed along to Mr. Papadopoulos, as the criminal complaint details his continued communications with the two Russian contacts.

Mr. Papadopoulos and the Russian woman spoke numerous times over Skype about a potential campaign-related foreign policy trip to Russia.

During one email exchange, the Russian woman wrote in an email to Mr. Papadopoulos that “we are all very excited by the possibility of a good relationship with Mr. Trump. The Russian Federation would love to welcome him once his candidature would be officially announced.”

During conversations with the Russian Foreign Ministry contact, he continued to pursue an “off the record” between campaign representatives and Russian government officials through at least August 2016.

When Mr. Papadopoulos was interviewed by FBI agents in January, he downplayed his interactions with the professor, stating that the man was “just a guy talk[ing] up connections or something.”

When asked whether he had been introduced to any Russian nationals or even anyone with Russian accent during the campaign, Mr. Papadopoulos failed to disclose the meetings with the professor or the Russian foreign ministry official.

He did disclose meeting the Russian woman, but said their communications were inconsequential.

Within a month of being interviewed by the FBI, Mr. Papadopoulos deactivated his Facebook account, which the complaint states he had used to communicate with both the foreign ministry contact and the professor. He also stopped using his old cellphone number and obtained a new phone number.

• S.A. Miller contributed to this article.