A Russian American tech entrepreneur and his wife, an aspiring rapper, have reached a plea agreement over a scheme to launder billions of dollars in cryptocurrency stolen from one of the world’s largest virtual currency exchanges, according to court records.

The couple, Ilya Lichtenstein and Heather Morgan, are scheduled to appear for a plea hearing and arraignment before Judge Colleen Kollar-Kotelly of the Federal District Court in Washington, D.C., on Aug. 3, according to an entry added to the court docket in the case on Friday.

The docket entry did not include details of the plea agreement, only that a copy of it needed to be provided to Judge Kollar-Kotelly along with other paperwork by July 27.

Lawyers for Mr. Lichtenstein and Ms. Morgan did not immediately respond to requests for comment, nor did the Justice Department.

Mr. Lichtenstein, 35, and Ms. Morgan, 33, were charged in February 2022 with conspiring to launder 119,754 Bitcoin that were worth $71 million when hackers stole them from the exchange Bitfinex, based in Hong Kong, in a 2016 heist that shook the cryptocurrency world. The couple were not charged with participating in the theft.

The exchange breach was one of several that resulted in large amounts of digital currency being stolen. The thefts, some of which drastically affected cryptocurrency values, underscored the security vulnerabilities of Bitcoin and other digital currencies.

Because such currencies move through decentralized computer networks that are not under the control of any single government or company, most trading occurs on largely unregulated exchanges that give consumers little information about their operations. The lack of regulation has led to a host of problems in the virtual-currency world.

Bitcoin’s value soared in the years between the Bitfinex heist and the arrest of Mr. Lichtenstein and Ms. Morgan. In announcing the charges against the couple, officials said they had seized $3.6 billion worth of the currency from them in what was then the Justice Department’s largest financial seizure ever. (The total value of the stolen Bitcoin had climbed to $4.5 billion by then, officials said.)

According to court documents, the hacker who breached Bitfinex’s systems initiated 2,000 transactions to send the stolen currency to a digital wallet under Mr. Lichtenstein’s control. Over five years, prosecutors said, about 25,000 digital tokens were transferred out of his wallet in a complex series of transactions meant to obscure their origin.

The couple’s laundering efforts, prosecutors said, included opening accounts under false names; moving stolen funds in small sums in thousands of transactions to avoid detection; using computers to automate their transactions; spreading funds across virtual-currency exchanges; and using U.S. business accounts to conceal their illegal activity.

Mr. Lichtenstein and Ms. Morgan used some of the stolen Bitcoin to buy gold, nonfungible tokens and prepaid debit cards, prosecutors said. A $500 card bought from Walmart was used to pay Uber and Hotels.com charges and buy a PlayStation, according to court documents.

When the couple were arrested, they were living in a two-bedroom condominium on an upper floor of a 42-story luxury building at the intersection of Wall and Water Streets in Lower Manhattan, records showed.

Mr. Lichtenstein, whose nickname is “Dutch,” has both American and Russian citizenship and has described himself as a tech entrepreneur, according to court documents.

Ms. Morgan has described herself on social media sites as “a serial entrepreneur” and an “irreverent comedic rapper” who calls herself “Razzlekhan” and the “crocodile of Wall Street.”

She also wrote magazine articles, including one for Forbes on how to “protect your business” as “cybercriminals and fraudsters are taking advantage of disruptions caused by the pandemic.”

Susan C. Beachy contributed research.