The defender, who turns 23 next Tuesday, is the fourth summer signing for the Blues as he joins Eden Hazard, Oscar and Marko Marin at Stamford Bridge. That attacking trio cost Chelsea a total of £64m, with Belgian playmaker Hazard accounting for half of that sum.
With Marseille expected to receive a fee of £7m for the attacking full-back, that brings Chelsea's outlay since winning the Champions League in May to £71m.
It will increase yet again as the West London club have had a fifth bid for Wigan Athletic forward Victor Moses accepted, while they are also expected to bring in another striker before next Friday's transfer deadline, with Porto's Hulk still linked to the club.
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.
Azpilicueta came up through the youth ranks of Osasuna in his native Pamplona, where he played for three years in the first team before making the £5.5m move to France in 2010. 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.
Azpilicueta made the last of his 69 appearances for Marseille in last weekend's 2-0 victory over Sochaux.
Although he is yet to be capped by the senior Spanish side, Azpilicueta has represented his country at all youth levels including as part of the Under-23 side at this summer's London Olympics.