Azpilicueta has joined Atletico after the Premier League club agreed to let him go with 12 months left on his contract.
He 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 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.
"Cesar leaves an everlasting mark at Chelsea, as a warrior, as a champion, and as a loyal Chelsea legend," the west London club's chairman Todd Boehly and co-controlling owner Behdad Eghbali said in a joint statement.
"He has set the standards at the club for more than a decade and demonstrated to everyone what is required day in, day out to achieve success."
The Champions League, Premier League, Europa League, FA Cup and League Cup winner was linked with a move to Serie A side Inter Milan before deciding on Atletico as his next destination.
He joins a growing list of players to leave Stamford Bridge this close season after the exits of Kalidou Koulibaly (32), N'Golo Kante (32) and Edouard Mendy (31), who all joined Saudi Pro League clubs.
Kai Havertz (24), Mateo Kovacic (29) and academy product Mason Mount (24) have signed for rivals Arsenal, Manchester City and Manchester United, respectively.
Chelsea have signed forwards Christopher Nkunku (25) and Nicolas Jackson (22) as they seek to revive their fortunes under former Tottenham Hotspur manager Mauricio Pochettino after finishing 12th last term - their worst finish to a season since 1994.
