The west Londoners have long been linked with a move for the Spaniard as they look to boost their options at right-back after Jose Bosingwa left the club this season.
The representatives for the 23-year-old have touched down in London to finalize the details of his contract, with relatives of the player proclaiming the transfer a “mere formality”.
Chelsea are expected to pay Marseille between €8 and 10 million for the services of the defender, who will sign a four or five-year contract at Stamford Bridge.
Azpilicueta, who has never been capped for his country's senior team, joined Marseille from Osasuna in 2010 for an estimated €7m fee.
Chelsea get their Premier League campaign under with a trip to Wigan on Sunday, with kick-off scheduled at 14:30CET.