President Donald Trump tweeted about the incident, saying: "Five Most Wanted leaders of ISIS just captured!". Jamal was shown on Iraqi state television on Wednesday night, wearing a yellow prison uniform.
Iraqi authorities on Wednesday said Iraq's global airports and border crossings would be closed from midnight Friday, ahead of the parliamentary election on Saturday.
Iraq's external intelligence agency published a statement confirming the arrests, but did not mention any details of the role played by the Americans or the Turks.
Eithawi was first reported to have been captured in a town east of Istanbul in February, after being tracked entering Turkey from Syria under his brother's name.
Iraqi security forces pull down a flag belonging to Sunni militant group ISIS.
Iraqi and U.S. intelligence spent several weeks interrogating Abu Zeid to acquire information about the location of the other leaders, who were in hiding.
The US-led coalition used this information to launch an airstrike in mid-April that killed 39 suspected ISIS members near Hajin, in the Deir el-Zour district of Syria, the second official said. After American and Iraqi intelligence agents extracted banking and communication codes from Ithawi's phone, Iraqi agents lured the other men into their trap and arrested them.
The terrorist, who was in charge of making bank transfers into the accounts the IS maintains in different countries and one of Abu Bakr's closest confidants, was captured by Turkish authorities and handed over to Iraq.