The French south coast club said on its website that the transfer was "officially concluded on Friday morning... and the Spaniard had signed a contract", while Chelsea said separately that the right-back had inked a two-year deal.
Chelsea boss Roberto Di Matteo said on the club's website: "Azpilicueta will give us cover at right-back. It gives us more options for the future.
"His signing gives us competition for positions. We'll see who will be first choice."
According to news reports, Azpilicueta's deal is worth eight million euros (£6.3 million, $10 million) but neither club disclosed the fee.
Azpilicueta was a June 2010 signing from Spanish club Osasuna but in November that year he ruptured anterior cruciate ligaments in his left knee during a match against Montpellier.
He returned to action at the start of last season and went on to play 30 matches in the French top flight, as well as eight matches in the Champions League.
In the close season, he was a member of Spain's Olympic football squad.
Marseille are offloading a number of players with a view to rebuilding and have recently seen the departure of French midfielder Alou Diarra.
Cameroon playmaker Stephane Mbia is also being courted by a number of English clubs.
Marseille coach Elie Baup is expecting new recruits to fill the gaps but has so far only seen the arrival of midfielder Florian Raspentino from Nantes in the close season.
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