Jihan Hanan, director of the Kurdish-administered camp, said that "there are approximately 850 people departing today".
She added that since the start of the year, about 10,000 Iraqis have left Al-Hol in 11 batches.
Kurdish-run camps and prisons in Syria's northeast hold tens of thousands of people, many with alleged or perceived links to IS, more than six years after the group's territorial defeat in Syria.
Al-Hol is northeast Syria's largest camp, and its residents have been living in dire conditions.
Umm Mahmud, 60, an Iraqi woman departing the camp, told AFP: "We've suffered greatly in Al-Hol, psychologically, physically and financially."
"Look at the children, look how happy they are. It's like a holiday," she said.
Hanan said the camp now housed approximately 27,000 people, including some 15,000 Syrians and about 6,300 foreign women and children from 42 nationalities, in addition to some 5,000 Iraqis.
While many Western countries refuse to take back their nationals, Baghdad has taken the lead by accelerating repatriations and urging others to follow suit.
In February, Kurdish official Sheikhmous Ahmed said the administration aimed to empty camps in Syria's northeast of thousands of displaced Syrians and Iraqi refugees, including suspected relatives of jihadists, by the end of the year.
IS seized swathes of Syria and neighbouring Iraq in 2014, before being territorially defeated in Syria in 2019, but has since maintains a presence there, particularly in the country's vast desert.
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