One child would return to Russia and five children would be reunited with their families in Ukraine, Russia's presidential commissioner for children's rights Maria Lvova-Belova said in a post on Telegram.
The US first lady wrote to Russian President Vladimir Putin in August about the plight of Ukrainian children separated from their families by the war.
Ukraine accuses Russia of abducting thousands of children, which Russian officials deny.
The White House, in a separate statement, said discussions continue with both countries, noting that it was the third time the first lady had brokered such a repatriation.
Lvova-Belova, in her post on the messaging app, thanked Melania Trump for her "unwavering commitment and active participation in reuniting children with their families".
Meanwhile, German Defence Minister Boris Pistorius said on Thursday that his country will deliver five additional PAC-3 missile interceptors to Ukraine if other countries donate a total of 30.
PAC-3, or Patriot Advanced Capability-3, is among the main weapons Ukraine's allies have supplied it as it fights Russia's invasion.
"We all know it is about saving lives," Pistorius said in Brussels after a meeting of the Ukraine Defence Contact Group.
"It's a matter of days and not a matter of weeks or months," he added.
The minister noted that the Patriots announcement has not been approved by governments yet but he said he is "very optimistic" the 30+5 can be achieved.
UK Defence Secretary John Healey said Ukraine's allies should make sure 2026 is the year Russia's war against the country ends.
Healey said in Brussels Ukraine's allies were "more united and more determined than ever".
He said: "We will step up military assistance to Ukraine. We will step up pressure on Russia.
"And we want to make 2026 the year this war ends, the year we secure peace."
with PA
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