Prosecutors laid out the plea agreement in a nine-page filing in New York federal court.
The Justice Department charged Cohen for telling House and Senate committees last year that a plan to build a Trump Tower in Moscow ended in January 2016. Thursday's filing said development continued after that date.
Trump has said multiple times he had no business dealings in Russia -- and Cohen told lawmakers he never contacted anyone in Russia about the real estate project. The filing Thursday said Cohen, in fact, spoke on the phone with a Russian intermediary for help with the development.
Cohen also admitted to discussing the deal with Trump, identified in the court document as "Individual 1," on three occasions and briefing family members involved in the Trump Organization.
The documents say Cohen lied to lawmakers out of loyalty and to minimize ties with Russia during Trump's campaign. The investigation, led by special counsel Robert Mueller, is trying to determine if Moscow interfered in the 2016 U.S. election and whether any members of Trump's campaign were involved.
Trump was asked about Cohen on Thursday as he left the White House for a trip to Argentina for the G20 summit.
"This was a deal [for a Trump Tower in Moscow] that didn't happen," he said, adding of Cohen: "He's a weak person and not a very smart person. What he's trying to do is very simple, he's got himself a big prison sentence and he's trying to get a much lesser prison sentence by making up a story.
"Even if he was right, it doesn't matter because I was allowed to do whatever I wanted during the campaign."
The case marks the first time Cohen has been charged in connection with the Mueller probe, and the second time he was charged in federal court this year. In August, he pleaded guilty to eight counts that included breaking campaign finance laws. Those charges were brought by U.S. attorneys in Manhattan. In a plea deal in that case, Cohen disclosed that he made a $130,000 payment to adult film star Stormy Daniels so she wouldn't discuss a prior sexual relationship with Trump.
The president has denied he ever had an affair with Daniels.
Although Thursday's agreement doesn't specify cooperation, Cohen has been interviewed numerous times by Mueller's investigators.
"Mr. Cohen has cooperated," Cohen's attorney said as he left the Manhattan court Thursday. "Mr. Cohen will continue to cooperate."
Sentencing guidelines for Cohen's charges would normally send a person to prison for up to six months. Prosecutors said in Thursday's filing they won't seek punishment outside that range, if he keeps cooperating.