Trump said in a Sunday morning news conference that Baghdadi fled from U.S. military personnel during the Saturday operation and detonated a suicide vest in a dead-end tunnel, killing himself and three children.
An on-site DNA test confirmed Baghdadi's identity.
"No personnel were lost in the operation," Trump said, "while a large number of Baghdadi's fighters and companions were killed with him."
He said two wives of Islamic State fighters wearing undetonated suicide vests were killed in the operation.
The president said Baghdadi had been under surveillance for weeks leading up to the operation, which involved the assistance of Russia, Turkey, Syria, Iraq and Syrian Kurds.
Trump told reporters that he did not inform House Speaker Nancy Pelosi of the raid, suggesting that doing so may have cost U.S. lives.
"I wanted to make sure this kept secret," he said. "I don't want to have men lost -- and women. I don't want to have people lost."
Pelosi, D-Calif., while congratulating the U.S. military who conducted the raid for their "heroism, dedication and skill," criticized Trump's move to notify Russia of the maneuver before government leaders.
"The House must be briefed on the raid, which the Russians but not top congressional leadership were notified of in advance," she said in a statement.
Rep. Eliot Engel, D-N.Y., chairman of the House Committee on Foreign Affairs, chastised Trump for thanking both Russia and Syria in their support, saying in a statement that both nations destabilized the region, which helped create the conditions for extremism to rise.
He also said he was "extremely troubled" that Trump only informed Republicans of the raid and by his suggestion that Pelosi can not be trusted with the information, calling it "tremendously problematic and insulting" and that it further politicizes foreign policy.
Newsweek reported Trump one week ago approved a special operations mission in the last bastion of the country's Islamist-dominated opposition.
The Kurdish-led Syrian Democratic Forces described a "successful" joint operation with the United States, CNN reported. The CIA assisted in locating the Islamic State leader, a defense official told CNN.
And Iraqi Joint Operations "played an important role in providing important information to the American side in the operations of killing al-Baghdadi," said Maj. Gen. Tahseen al-Khafaji, a spokesperson for the Iraqi Joint Operations.
In 2010, Baghdadi became the leader of Islamic State of Iraq, known as ISIS, ISIL and Daesh.
The Islamic State declared it absorbed an al-Qaida-backed militant group in Syria in 2013.
Osama bin Laden, the founder and first leader of the Islamist terrorist group al-Qaida was killed in Pakistan on May 2, 2011, by U.S. Navy SEALs.
Baghdadi was last seen in July 2014, when he spoke at the Great Mosque in Mosul, Iraq.
In February 2018, several U.S. officials said Baghdadi had been wounded in an airstrike in May 2017.
In April, the Islamic State media wing al-Furqan displayed a man purporting to be Baghdadi.
The U.S. State Department had offered a $25 million reward for information on his whereabouts.
"Baghdadi is probably moving around a lot to avoid detection," Jeffrey Simon, a terrorism expert and founder of the national security consultancy firm Political Risk Assessment Inc., told Fox News earlier this year. "But it will just be a matter of time before he is found.
"I believe that he is still alive. News of his death would have been hard to keep secret for very long."