Laporte has reportedly agreed to join Al-Nassr after five-and-a-half-years in England.
The Spain international will become the latest high-profile player to sign for a Saudi Pro League club, with ex-City team-mate Riyad Mahrez among them after making the move to Al-Ahli last month.
“Dear Cityzens, today I wanted to share a story with you,” Laporte said in a video on Twitter that went on to show a highlights reel of his time at Man City.
“This is now our history. Thank you and see you really soon.”
Centre-back Laporte added in his social-media post: “It has lasted for five-and-a-half unforgettable years.
“Plenty of memories that I will keep forever close to my heart.”
Laporte will leave the Etihad after making 180 appearances for City, with his last outing for the club off the bench during their opening-day Premier League win at Burnley.
After being restricted to a place among the substitutes for the Community Shield defeat to Arsenal and the UEFA Super Cup triumph over Sevilla, he was absent from the matchday squad for last weekend’s win over Newcastle.
The arrival of Josko Gvardiol from RB Leipzig has further pushed Laporte down the pecking order at City.
A powerful recruitment drive by Saudi Arabia’s Public Investment Fund has seen Saudi Pro League teams – all PIF-owned – sign a plethora of the world’s best players this summer.