The group, who had travelled for nearly 12 hours from Belarus, came straight to the President's home from Dublin Airport for a surprise visit.
"This reminds you what Christmas is all about and the chaos that we can get involved in, this is the joyful side," said Ms Hewson. "It's a very feel-good story."
"It's a culmination of seeing all the hard work that everyone has put into this, to get these children here for Christmas."
Dozens of families from around Ireland will host the children, many of whom come from mental institutions or orphanages, over the next three weeks.
"The host families are amazing. A lot of the people are just ordinary people, not nurses or physiotherapists or anything, they just seem to have a special gift," said Ms Hewson, who is board member of Chernobyl Children International (CCI).
Ms O'Donnell added: "The families look forward to receiving these kids; it's a huge commitment as many of them have certain special needs so it can be difficult to mind them, but they love it."
Ms O'Donnell also stressed the importance of keeping the Chernobyl issue alive. "It's very easy for people to forget and think of it as a historic tragedy. But, in fact, the implications of the explosion are living on through the gene pool. Over 6,000 children are still born with cardiac defects."
"This is really Christmas for me, not December 25," Ms Roche, CEO of CCI, told the Irish Independent.
"It's about hope, love and compassion and this is a reflection of the compassion and generosity of our President."
She added: "The Aras is the heart of the nation and to see it opened up for these children is just phenomenal. Ireland still has that room to extend that hand of friendship."
CCI has spent more than €92m on humanitarian and medical aid programmes in Belarus, Ukraine and Russia since 1986.