A prosecutor said van der Zwaan, who is a Dutch national, worked closely with Gates and another person who is based in Ukraine on that report.
Van der Zwaan entered his guilty plea in U.S. District Court in Washington.
Judge Amy Jackson agreed to sentence van der Zwaan on an expedited basis because his wife, Eva Khan, is pregnant and living in London.
Eva Khan, an art critic who married van der Zwaan last year, is due to deliver their child in August. She is the daughter of German Khan, a Russian oligarch who is suing research firm Fusion GPS over a dossier alleging salacious and unverified ties between President Donald Trump and Russia. The private intelligence-gathering firm's now-infamous dossier was compiled by former British spy Christopher Steele.
Khan and two other Russian investors in the financial institution Alfa Bank filed a libel suit against the firm last fall, claiming the dossier damaged their reputations.
Van der Zwaan faces a sentence of up to five years in prison and a $250,000 fine.
But given his background and his cooperation with Mueller's probe, van der Zwaan is more likely to be sentenced to six months or less, with possibly no jail time at all, and anywhere from a $500 to $9,500 fine.
The FBI is holding van der Zwaan's passport. For now, his travel is limited to within Washington, but he will be allowed to travel to New York on two days' notice.
The charges were levied on the same day the special counsel announced a surprise indictment against 13 Russian individuals and three entities alleged to have waged a campaign of "information warfare" against the U.S. in the 2016 presidential election.
Skadden, in a statement to CNBC, said, "The firm terminated its employment of Alex van der Zwaan in 2017 and has been cooperating with authorities in connection with this matter."