Azpilicueta, 22, who has represented Spain at several youth levels and played at the Olympics this summer, missed Marseille's Europa League qualifier against FC Sheriff Tiraspol on Thursday night as he travelled to London to complete the deal.
Marseille confirmed the move in a statement on their website. "Cesar Azpilicueta transfer to Chelsea's is official. The Spanish defender has signed with the Champions of Europe 2012," the statement said.
Not long after, Chelsea revealed the news with a statement on their own website. It read: "Chelsea Football Club is delighted to announce the signing of Cesar Azpilicueta.
"The 22-year-old right-back, who recently represented Spain at the London Olympics, arrives at Stamford Bridge following a two-year spell in France's Ligue 1 with Marseille."
Azpilicueta made the last of his 69 appearances for Marseille in last weekend's 2-0 victory over Sochaux.
He joined the French club in 2010 from Osasuna, and although he suffered a serious knee injury in his first season on the Mediterranean coast, he went on to establish himself as the club's first-choice right-back.