The US-backed Syrian Democratic Forces' victory in the remote riverside village of Baghouz, where IS made its last stand, capped a six-month operation against the final remnants of IS-controlled territory that once stretched across a vast swathe of Iraq and Syria, with seven million people in its sway.
"We will remain vigilant... until it is finally defeated wherever it operates," Trump said of IS in a statement.
"The United States will defend American interests whenever and wherever necessary. We will continue to work with our partners and allies to totally crush radical Islamic terrorists."
Trump also had a warning for youths who can easily be swayed.
"To all of the young people on the internet believing in ISIS's Propaganda, you will be dead if you join. Think instead about having a great life," he said, using an alternative acronym for the jihadist movement.
Acting US Defense Secretary Patrick Shanahan welcomed the "critical milestone," but warned that "our work is far from complete."
"We will continue our work with the global coalition to deny ISIS safe haven anywhere in the world," he said.
"We remain committed to ISIS's enduring defeat and we are confident that we will prevail."
Chairman of the Joint Chiefs of Staff General Joseph Dunford, Jr added that "the US military remains committed to working closely with our Coalition and regional partners to ensure the lasting defeat of ISIS."
The jihadists retain a presence in eastern Syria's vast Badia desert and various other hideouts from which they could wage the kind of deadly guerrilla insurgency that accompanied the rise of IS.
While the geographic caliphate has been dismantled, analysts warn remnants of the group can melt back into the population while seeking to convert others to their ideology.
The sanctioned individuals include people who work with the Shahid Karimi Group, which the Treasury Department said focused on missile and explosives projects for SPND, and the Shahid Chamran Group, which researches electromagnetics and wave generation.
The US official said that the SPND was still in place and headed by Mohsen Fakhrizadeh, a physicist identified by US and Israeli intelligence as the aspiring father of Iran's nuclear bomb.
"It's as if some evil version of Robert Oppenheimer had been kept in charge of keeping the Manhattan Project crew together years afterwards," the official said, referring to the founder of the US nuclear program in World War II.