The 28-year-old defender joined Palace in the summer of 2021 and made 113 appearances for the club in all competitions, scoring three goals and registering six assists.
Andersen was part of the side which reached the FA Cup semi-finals at Wembley in 2021/22, and memorably scored the winning goal against Manchester United at Old Trafford last season.
The defender played in all 38 of Palace’s Premier League matches in 2023/24, marking his 100th appearance for the club with a clean sheet in a 3-0 win over Burnley in February. He shared the Players' Player of the Season award with Jean-Philippe Mateta.
Chairman Steve Parish said: “Joachim has been immense for the club over his three years at Palace, playing a part in some of our most memorable recent results.
“He leaves with the utmost respect of everyone here, and we wish him well for the future.”