Live updates: Trump confirms Baghdadi killed
Predictably, the United States' allies have been lining up to congratulate the US on its operation.
British Prime Minister Boris Johnson called Baghdadi's death "an important moment".
Meanwhile the French Defence Minister said Baghdadi had been handed an "early retirement".
Translation: "Baghdadi: early retirement for a terrorist, but not for his organisation. I congratulate our American allies with this operation. My thoughts thoughts today are for all the victims of the madness of Bagdhadi and the criminals who have followed him."
However Mohammad Javad Azari-Jahromi, Iran's information minister, sounded unimpressed.
"Not a big deal, You just killed your creature," he tweeted, accusing the US of being responsible for Baghdadi's rise.
Baghdadi was born Ibrahim Awad al-Samarrai in 1971 near the Iraqi town of Samarra, as the third of four sons to a Quran teacher who claimed to be a descendent of the Prophet Muhammad.
Apparently a quiet young man who studied Islam and played football, he became one of the most wanted men in the world when in 2014 he declared from Mosul's al-Nuri Mosque that he was ruler of all the land IS had conquered in Syria and Iraq.
Under his leadership, Islamic State murdered thousands and terrorised millions across the world. Middle East Eye takes a look at the now-dead militant here: Abu Bakr al-Baghdadi: The 'loner' who became leader of Islamic State
Trump claimed before and after Baghdadi's killing that the Islamic State group had been destroyed and defeated, but how accurate is that?
Mazloum Abdi, head of the Kurdish-led Syrian Democratic Forces militia that rolled IS back with US backing, said he expects a backlash.
"Sleeper cells will seek revenge for Baghdadi's death," he told the AFP news agency. "This is why anything is possible, including attacks on prisons."
The SDF holds thousands of suspected IS members prisoner in Syria, and has repeatedly raised concern about their security as Turkish forces have staged an assault in the Kurdish-held northeast.
Turkey, the Syrian Kurds and Iraq have all claimed knowledge of the operation, but it seems there may have been other players too.
Trump said Russia, Syria, Turkey and Iraq all assisted in preparations for the raid, which required flying over an hour by helicopter in both directions from an undisclosed base.
The US forces "executed a dangerous and daring nighttime raid in northwestern Syria and accomplished their mission in grand style", Trump said, adding that a US dog was wounded.
“The canine, a beautiful dog, a talented dog, was injured and brought back,” he said.
Speaking to reporters, Trump said Baghdadi "died after running into a dead-end tunnel, whimpering and crying and screaming all the way".
"His body was mutilated by the blast. The tunnel had caved in on it in addition. But test results gave certain immediate and totally positive identification. It was him," the president said.
"The thug who tried so hard to intimidate others spent his last moments in utter fear, in total panic and dread, terrified of the American forces bearing down on him."
"No [US] personnel were lost in the operation while a large number of Baghdadi's fighters and companions were killed with him," Trump added.
US President Donald Trump has confirmed that Abu Bakr al-Baghdadi is dead. He blew himself up using a suicide vest during a US special forces raid, Trump said.
No US personnel were lost in the operation, he said, though many of Baghdadi's companions were killed.