The mission will be conducted under the auspices of the International Committee of the Red Cross. The organization said in a statement it is ready to facilitate the operation with the involvement of all sides concerned following a Russian initiative to provide humanitarian assistance to people in eastern Ukraine.
It wasn't clear when the deliveries would start.
"The practical details of this operation need to be clarified before this initiative can move forward," said Laurent Corbaz, the ICRC's head of operations for Europe and Central Asia.
Moscow had long urged Kiev to allow the aid delivery, but Ukraine and the West previously had opposed the move, fearing that it could serve as a pretext for sending Russian troops into rebel-held territory. Ukraine and the West have accused Moscow of arming and supporting the rebels fighting government troops in the east, a charge that the Kremlin has denied.
The Red Cross said it has shared a document with Ukrainian and Russian authorities that stipulates all parties must guarantee the security of its staff during the operation and respect the organization's neutrality.
The aid mission was announced after a conversation between U.S. President Barack Obama and Ukrainian President Petro Poroshenko Monday.
The White House said that Obama and Poroshenko agreed that "any Russian intervention in Ukraine without the formal, express consent and authorization of the Ukraine government would be unacceptable and a violation of international law."
Shortly before that, Russia had declared that it was dispatching a humanitarian convoy into Ukraine in cooperation with the Red Cross without giving any details. President Vladimir Putin's spokesman, Dmitry Peskov, later was quoted by Russian news wires as saying that the convoy wouldn't involve and military personnel.
Officials in Kiev took pains to specify Monday that the Ukrainian government was behind the humanitarian convoy initiative, and that Moscow was only one of several countries involved.
"Apart from deliveries provided by Ukraine, the mission will feature an international component, including aid provided to the International Committee of the Red Cross by the United States, the EU, as well as Russia," Ukraine's Foreign Ministry said.
The ministry also laid out specific conditions for the aid shipment, saying it should only pass through checkpoints controlled by the Ukrainian government. At least 100 kilometers (60 miles) of the long Russian-Ukrainian border is currently in rebel hands.
It said that the aid will be distributed by the Ukrainian authorities in the Luhansk region, one of the two mostly Russian-speaking rebel provinces.
Some of the heaviest impact on civilians has been seen in Luhansk — the rebel-held capital of the Luhansk province that had a pre-war population of 420,000. City authorities said Monday that the 250,000 residents remaining have had no electricity or water supplies for nine days.
Food, medicine and fuel are also not being delivered, the Luhansk city government said.
"Humanitarian aid will only be distributed among the civilian population of the Luhansk province, which has long been suffering from the actions of illegal armed gangs," the ministry said in a statement.
In the last week, Ukrainian government forces have been closing on the few remaining rebel strongholds, including Donetsk, the largest rebel-held city. Hundreds of thousands have been fleeing the fighting in the city, which had a population of 1 million before the hostilities.
Russian Foreign Minister Sergey Lavrov criticized the West for its reluctance to support the delivery of Russian aid earlier, but voiced hope for the success of the mission. "I hope that our Western partners will not put a spanner in the works," he said.
Alexander Zakharchenko, the leader of the self-proclaimed rebel government in the Donetsk region, said Monday that the insurgents were ready to observe a cease-fire to allow humanitarian aid to pass into Luhansk.
The talk about the relief mission came as fierce fighting continued to rage in the east.
Donetsk city council spokesman Maxim Rovinsky said a rocket hit a high-security prison Monday, killing at least one inmate and leaving three others severely wounded. In the chaos, 106 prisoners escaped, including some jailed for murder, robbery and rape, he said.
Officials with Ukraine's state penitentiary service said later Monday that 34 prisoners had returned to the jail. It was not immediately possible to verify that claim.
One of the prisoners who had apparently returned to the prison told The Associated Press that inmates were forced to flee to avoid incoming rockets, but were apprehended in a nearby neighborhood.
Both Ukrainian government forces and the pro-Russian rebels have deployed heavy Soviet-built weapons that lack precision. Apartments and other civilian buildings have frequently been hit, adding to the mounting death toll among civilians.
Many of those in Russian-speaking eastern Ukraine distrust the new central government in Kiev, which came to power after the February ouster of former President Viktor Yanukovych, whose power base was in eastern Ukraine.
Fighting began a month after Russia annexed Ukraine's peninsula of Crimea in March.
Leonard reported from Kiev. Vladimir Isachenkov in Moscow and John Heilprin in Geneva also contributed to this report.
Copyright 2014 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.