The documents and other items should have been turned over to the agency, according to the report.
The recovery of the documents followed discussions between the Archives and Trump’s lawyers that began last year, according to the newspaper.
The items included correspondence with Chairman Kim, dubbed "love letters" by Trump, and a letter left for him as successor by President Barack Obama.
The newspaper went on to say that the retrieval of the boxes raises concerns about Trump’s adherence to the Presidential Records Act, requiring preservation of memos, letters, notes, emails, faxes and other written communications related to a president’s official duties.
Trump advisers deny any malign intent, according to the newspaper.
In 2018 Trump, in an interview with The Washington Post, referred to his correspondence with Kim as "love letters." He noted the messages from Kim were evidence of their productive relationship.
Despite meeting three times during Trump's tenure in office, the two failed to resolve the nuclear crisis on the Korean Peninsula after negotiations broke down following a summit in Vietnam due to differences over lifting sanctions.