Azpilicueta has joined Atletico after the Premier League club agreed to let him go with 12 months left on his contract.
The 33-year-old returns to Spain after 13 years, where he last spent three seasons at Osasuna from 2007-2010.
Azpilicueta was a mainstay at Chelsea after arriving from Ligue 1 side Olympique de Marseille in 2012, making more than 500 appearances in all competitions, scoring 17 goals, providing 56 assists and winning every major title with the club.