Under the terms of the deal, Kiev will hand over 306 prisoners to the rebels and receive 74 prisoners in return, according to the report.
On Nov. 15, Putin made his first official contact with the heads of the breakaway republics and urged separatist leaders, including Oleksandr Zakharchenko, to exchange prisoners with the Ukrainian government.
The exchange of prisoners could affect 380 people in eastern rebel area of Ukraine.
"My son rang", the mother of a Ukrainian prisoner Oleksandr Oliynyk told the Ukrainian news channel 112.
By day's end, the Ukrainian government will carry out a prisoner swap with the self-proclaimed Donetsk republic.
On Tuesday, Poroshenko met with the relatives of the hostages, saying: "Nothing is more important than to return our people home", according to a presidential statement.
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A prisoner waves during the exchange. Moreover, ten days ago, Russia withdrew its officers from Joint Centre for Ceasefire Control due to Kiev's new bureaucratic demands that oblige all Russian citizens to provide information prior to any trip to Ukraine.
According to Poroshenko, among the prisoners handed to Ukraine were a historian and a "cyborg" - the nickname Ukrainians gave to soldiers who defended Donetsk airport in one of the conflict's most intense battles in 2014.
Ukraine's eastern Donetsk and Luhansk regions have been mired in conflict since separatists declared their independence from Kiev in spring 2014, shortly after Russia's controversial annexation of Ukraine's Crimea region.
There was no immediate comment from the authorities in Moscow, which Ukraine and its Western allies accuse of supporting the pro-Russian separatists with troops, cash and heavy weapons, an accusation Moscow denies.
"This would be a very serious step in the implementation of the Minsk agreements and issues of peace in the Donbas region", said Viktor Medvedchuk, leader of the Kremlin-aligned "Ukrainian Choice" group.
The Minsk agreements, which have never been fully implemented, were brokered in early 2015 by German Chancellor Angela Merkel and French President Francois Hollande in talks between Russia, Ukraine, France and Germany.