In Chelsea transfer news, the 33-year-old Spain defender won every available honour at Stamford Bridge, including two Premier League titles and the Champions League.
Azpilicueta had 12 months left on his Chelsea contract.
"It is difficult to express how I feel, it has been incredible," he said.
In a social media video posted by the club, a tearful Azpilicueta added: "I feel I gave everything. I love it.
"I think it would be pretty obvious to pick the highest moment of my career, when we won the Champions League in Porto. It was my first trophy as captain.
"Chelsea is my home, it always will be and hopefully I can come back in a different role."
Azpilicueta started out with boyhood club Osasuna and spent two years at Marseille before completing a £6.5m move to Chelsea in August 2012.
The full-back went on to score 17 goals in 508 appearances for the west London club, and succeeded Gary Cahill as captain in 2019.
In Chelsea transfer news, Azpilicueta is one of just six players to have won the Premier League, FA Cup, League Cup, Champions League, Uefa Super Cup and Fifa Club World Cup, while his 13 cup final appearances are a club record.
Capped 44 times by Spain, he has been a constant during a turbulent decade at Stamford Bridge that has seen 10 managers come and go, as well as a change in ownership.
Azpilicueta won the Premier League under Jose Mourinho in 2015 and again with Antonio Conte in 2017, and became only the second Chelsea skipper to lift the Champions League.
That was in 2021 when Thomas Tuchel's side beat Manchester City in the final, while he also won the Europa League twice in 2013 and 2019.
The Spaniard was linked with a move to Barcelona before signing a new two-year contract in August 2022, but has become the latest senior player to leave the club during what has been a transitional summer under new manager Mauricio Pochettino.
In other Chelsea transfer news, big-name departures have included Kai Havertz to Arsenal and Mateo Kovacic to Manchester City, while Manchester United have signed Mason Mount.
Goalkeeper Edouard Mendy, centre-back Kalidou Koulibaly and French defensive midfielder N'Golo Kante have also left to play in the Saudi Pro League.
