According to the coalition, the operation was done in coordination between Iraqi forces and the Kurdish-led Syrian Democratic Forces (SDF) across the border.
Al-Eithawi, a top aide to ISIS leader Abu Bakr al-Baghdadi, was captured in February by Turkish authorities and handed over to Iraqi agents, a security advisor to the Iraqi government said on Thursday.
"Five Most Wanted leaders of ISIS just captured!", Trump wrote on his official Twitter account, after the Iraqi state television on Wednesday said the country's intelligence agency lured the Daesh terrorists into crossing Syria and arrested them.
Their arrest represented the two highest-ranking ISIS jihadists ever to be captured alive.
The leaders were taken in Iraq after months of strategic planning by the US, including the CIA, Turkey and Iraqi forces.
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Adrian J.T. Rankine-Galloway, said the US credited Iraqi security forces with the militants' capture "on the Iraq-Syria border".
After Iraqi forces retook the Iraqi city of Mosul from IS last summer, Syrian forces on the other side of the border claimed a series of swift victories, but the campaign was stalled recently when Turkey launched a cross-border raid into Syria's north. The list does not included the leader of the IG Abu Bakr al-Baghdadi. He was also in charge of the education curriculum, and was a member of the body that appointed security and administrative leaders for the Islamic State's territory, which had included large parts of Iraq and Syria.
Last December, officials in Baghdad declared that Daesh's military presence in Iraq had been all but dismantled over operations backed by the USA -led International Alliance.