Trump says in a tweet that "Subject to the receipt of further information, I will be allowing, as President, the long-blocked and classified JFK FILES to be opened".
The National Archives has until Thursday to disclose the remaining files related to Kennedy's 1963 assassination.
The remaining files include more than 3,000 documents never seen by the public, as well as more than 30,000 files that were previously released with redactions.
Congress accelerated the choice to declassify them, and President Bush signed the Records Collection Act a year later.
What are the JFK files?
The anticipated release has had scholars and armchair detectives buzzing. Instead of squashing conspiracy theories, the release of the last files may just exacerbate them. "But what the files are doing and why they're important to come out is they fill in the history of the case and show us how the Federal Bureau of Investigation and Central Intelligence Agency repeatedly hid the evidence".
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Despite serious questions about the official inquest, and theories purporting that organised crime, Cuba or a cabal of USA security agents was involved, conspiracy theorists have yet to produce conclusive proof that Oswald acted in consort with anyone.
Oswald's stated reason for going was to get visas that would allow him to enter Cuba and the Soviet Union, according to the Warren Commission, the investigative body established by President Lyndon B. Johnson, but much about the trip remains unknown.
He said the release would be subject "to the receipt of further information". Phillips, Morley said, oversaw the agency's operations against Cuban president Fidel Castro and was deeply familiar with the CIA's surveillance of Oswald in Mexico City.
After the president announced his decision, Stone tweeted: "Yes! victory!"
The former chairman of the Assassination Records Review Board told Dallas News, "I don't think there are big revelations".
"There could be some jewels in there because in our level of knowledge in the 1990s is maybe different from today", Tunheim said.
The archives said 1 percent of roughly 5 million pages of assassination-related documents are still undisclosed, while another 11 percent of the released documents have had "sensitive portions" redacted.