Dutch investigators leading a probe into the disaster were preparing to take charge of the bodies of 280 victims set to arrive by train in the government-controlled city of Kharkiv.
The remains are to be taken to the Netherlands which had 193 citizens on board when the flight went down on Thursday, a disaster that has taken Ukraine's bloody three-month conflict to the doorstep of countries as far away as Malaysia and Australia.
The rebel concessions came as European foreign ministers were to meet in Brussels to weigh possible new sanctions against Russia for its perceived support of the insurgency rocking ex-Soviet Ukraine.
Both black boxes, which record cockpit activity and flight data, were handed to Malaysian officials by the prime minister of the self-proclaimed Donetsk People's Republic, Alexander Borodai, in front of scores of journalists.
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Borodai also announced a ceasefire within 10 kilometres of the site, hours after the pro-Western authorities in Kiev said they would halt all fighting in the zone.
International monitors were also finally given freedom to examine the vast crash site, littered with poignant fragments from hundreds of destroyed lives.
Despite the apparent progress in getting the investigation going, leaders warned the rebels' handling of the crash site had already done much damage.
Australian Prime Minister Tony Abbott, whose country lost 28 citizens and nine residents in the crash, said: "There is still a long, long way to go."
"After the crime comes the cover-up," he added. "What we have seen is evidence tampering on an industrial scale. That has to stop.