Trump said many ISIS terrorists had been killed in the raid and that Abu Bakr al-Baghdadi had detonated a suicide vest when he was cornered in a tunnel.
A USA military dog was injured in the tunnel where Baghdadi died, according to Mr Trump.
"He was a sick and depraved man and now he's gone", said Trump, adding that capturing or killing Baghdadi had been the top national security priority for his administration.
In announcing al-Baghdadi's death, he leaned into comparing the successful operation with the 2011 mission to kill 9/11 mastermind Osama bin Laden. Trump also agreed to keep about 150 US troops at a base in southern Syria. "When it comes to security, we are sure that we will secure this country", said its spokesman, Wawan Purwanto.
Trumps said the operation was carried out with "cooperation" from Russia, Iraq, Turkey and Kurdish forces in Syria.
The death of the Islamic State's leader in a daring nighttime raid vindicated the value of three traditional American strengths: robust alliances, faith in intelligence agencies and the projection of military power around the world.
Turkey's defence ministry said that Turkish and U.S. military authorities exchanged and coordinated information ahead of the attack.
Clint Watts of the Foreign Policy Research Institute wrote on Sunday that "al-Baghdadi's death will dash the dreams of an Islamic State centered in the Levant, but its years of operations recruited, trained and dispatched foreign fighters from dozens of countries that will lead the next generation of jihad to other frontiers".
"He reached the end of the tunnel as our dogs chased him down", Trump added. The explosion killed three of his children.
Baghdadi's body was "mutilated by the blasts", so U.S. forces had to use a DNA test onsite to confirm his identity.
"We went out in the balcony to see and they started shooting, with automatic rifles".
It is believed when United States forces left, they took the same route over militarised territory that they used when flying in. People can now think this a time for peace, is a time for us as Muslims to now relax.
He said at one point during his address to the nation on Sunday that the quality felt "as though you were watching a movie".
In addition to conducting high-profile attacks inside Afghanistan, the official said the Islamic State has also already proven its ability to inspire and enable terrorist attacks outside Afghanistan, including a deadly one in Sweden. The Turkish military also Tweeted that prior to the operation in Idlib, it exchanged "information" and co-ordinated with USA military authorities.
He also revealed that U.S. forces spent roughly two hours on the ground collecting "highly sensitive material", including information on IS's origins and its future plans.
The information about the terror leader's more specific whereabouts, the officials cited in the report said, came mostly from Syrian and Iraqi Kurds who continued to pass on the intelligence to the CIA, even after Trump announced the pullout - a move widely perceived to have been an abandonment of the US's Kurdish allies.
The president said helicopters transporting the special forces took off from an undisclosed location after 17:00 in Washington DC (21:00 GMT) on Saturday, when he and other leaders gathered at the White House Situation Room.
He has attempted to counter this opposition not only with the Baghdadi assassination, but also by sending United States troops back into Syria with the mission of "securing" the country's oil fields. But in 2017 the group lost control of Mosul in Iraq and Raqqa in Syria, and quickly thereafter nearly all of its territory, turning Baghdadi into a fugitive.