The handover came hours after the UN Security Council voted unanimously to demand immediate international access to the crash site.
EU foreign ministers will consider more sanctions against Russia on Tuesday.
The Malaysian Airlines passenger jet crashed last Thursday, killing all 298 people on board.
Western nations say there is growing evidence that flight MH17 was hit by a Russian-supplied missile fired by rebels, but Russia has suggested Ukrainian government forces are to blame.
EU foreign ministers, meeting in Brussels, are thought likely to discuss expanding the list of Russian officials targeted by sanctions, but have so far steered clear of targeting whole sectors of the Russian economy.
Both the EU and the US imposed sanctions on Moscow following its annexation of Crimea and the outbreak of hostilities in eastern Ukraine.
Experts say the “black boxes” will reveal the exact time of the incident and the altitude and precise position of the aircraft.
They should also contain the cockpit voice recorder, which it is hoped will provide clues as to what the cause of the crash was.
The head of the Malaysian delegation at the handover in Donetsk told reporters that the recorders were “in good condition”.
The handover followed talks between the rebel commander and self-styled Prime Minister of the Donetsk People’s Republic Alexander Borodai and the Malaysian PM Najib Razak, according to a statement of Najib Razak.
The Malaysian prime minister also said those talks led to the rebels agreeing to allow the bodies to be transported to Kharkiv and international investigators to access the area.
“In recent days, there were times I wanted to give greater voice to the anger and grief that the Malaysian people feel and that I feel,” he said.
“But sometimes, we must work quietly in the service of a better outcome.”
Pro-Russian rebels allowed a freight train carrying the bodies of 282 passengers to be moved from a town near the crash site to Donetsk on Monday.
The Malaysian experts and a Dutch delegation are travelling with the train to the city of Kharkiv, where it is expected to arrive later on Tuesday.
From there, the bodies will be prepared for transfer by air to the Netherlands where forensic experts will evaluate and identify them.
Meanwhile a UN resolution, proposed by Australia, was passed calling for a “full, thorough and independent international investigation” into the downing of the plane over Grabove on July 17.
It also demanded that those responsible “be held to account and that all states co-operate fully with efforts to establish accountability”.
TLyEX2DlzUAImage source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…