The report brings an end to a special counsel investigation that led to criminal charges, conviction and then a pardon by outgoing President Joe Biden.
Alexander Smirnov pleaded guilty in December to lying to the FBI about a phony bribery scheme that prosecutors say was an effort to influence the 2020 election.
Trump's team pointed to President Joe Biden's pardon of his son, saying it showed that Trump's "promise to end the weaponization of our justice system needs to happen."
The decision, which was first reported by NBC News, is a reversal for the president, who repeatedly said he would not use his authority to pardon his son or commute his sentence.