The 20-year-old, who has been dubbed the new Zinedine Zidane, has agreed a four-year contract and will join after Euro 2008, according to the BBC Sport Website.
Nasri, who made two appearances at Euro 2008 has spent four seasons with the French side and is believed to have a £13.5m buy-out clause in his contract.
Last season he scored six goals in 30 games for Marseille who qualified for the Champions League.
Arsenal past and present: Samir Nasri (left) will join Arsenal a year after Thierry Henry left the club
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London gets ready for the Diamond Jubilee - in pictures
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EXCLUSIVE: I won't play with Joey Barton, says Adel Taarabt
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Diamond Jubilee: Boat by boat, here is where to watch the Queen's Thames flotilla - VIDEO
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Duchess of Cambridge is pretty in pink at her first Buckingham Palace garden party
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News pictures of the day
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Locked up and banned: The Tube drunk whose vile racist rant was caught on film (video)
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London 2012 Olympics: Raising the bar and the Games haven't even started yet. Price of toasting Team GB is £6 a pint! -
Timebomb ticking in Thames Estuary could put Boris Island plans in jeopardy -
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‘We will form a human barricade to keep missiles off our homes’
Why I think doctors are right to strike 
Family pay tribute to the London man who gave his life to save a five-year-old girl from drowning 
Eton schoolboys fly Games flag on Everest 
Horror on the 5.53! Commuter dragged 200 feet after getting hand trapped on train 
Shrimpy's - review 
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