This follows a request by authorities in the Netherlands, from where the plane had flown before it was shot down over Ukraine.
The experts, based at Farnborough in England, will download data from the flight recorders for "international analysis".
All 298 people on board , including 10 Britons, were killed in the crash.
Cameron tweeted - "We've agreed Dutch request for air accident investigators at Farnborough to retrieve data from MH17 black boxes for international analysis".
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The UK Air Accidents Investigation Branch (AAIB) confirmed it would be working on the flight recorders which have been handed over by pro-Russian rebels.
The AAIB has one of only two specialist "replay units" in Europe - the other is in France - where they have the equipment to listen to the audio recorded on the flight.
Four speakers are used in a special room to create a surround-sound effect.