Laporte departs the Etihad Stadium after five-and-a-half years, having joined from Athletic Bilbao in January 2018.
He made 180 appearances in total for Manchester City and notably headed in the only goal of the game in the 2021 League Cup final against Tottenham Hotspurs.
The 29-year-old France-born Spain international leaves Manchester City with five Premier League titles, two FA Cups, three League Cups, the UEFA Champions League and UEFA Super Cup.
The defender shared an emotional farewell message along with a video that encapsulated his journey with City. He wrote: "Dear Cityzens, today I wanted to share a story with you. It has lasted for five and a half unforgettable years. Plenty of memories that I will keep forever close to my heart. It’s always easy to think of the good ones: the trophies, the wins, the goals, the tackles and the big fights in the Premier League. But I will also remember the bad ones: the injuries and being sidelined, the defeats and the mistakes I may have made.
"From trophies to setbacks, victories to injuries, it’s all been part of my journey, and I’m grateful for absolutely every moment that shaped me into who I am today. I want to thank everyone who made this journey possible: the Man City board, the coaches and the whole staff, every single teammate I shared the dressing room with, and of course all of you. It was an honor and a pleasure to wear these colors, and I hope you will remember me in a good way for this. Thank you again for everything. I wish you the best of luck for the future and I will always keep an eye on you guys. Until we meet again, Aymeric."