The 29-year-old defender is understood to have agreed a three-year contract with the Saudi Arabian club and completed his medical on Wednesday ahead of finalising his reported £23m move to the Middle East.
Laporte is set to depart Man City after five-and-a-half years at the Etihad Stadium, making 180 appearances across all competitions.
The Spain international has won a total of 13 trophies with the Citizens including five Premier League titles, three EFL Cups, two FA Cups, one Champions League, one Community Shield and one UEFA Super Cup, lifting the latter earlier this month after beating Sevilla on penalties.
Laporte has taken to social media to bid farewell to Man City supporters, posting a video along with the following statement: "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."
Laporte has been strongly linked with a exit from Man City throughout this summer after he struggled for game time under manager Pep Guardiola last season.
The centre-back started only 20 games across all competitions in City's 2022-23 treble-winning campaign, including just 11 Premier League starts, while he also watched on as an unused substitute on 22 occasions.
Ruben Dias, John Stones, Manuel Akanji and Nathan Ake were all preferred ahead of Laporte, while the big-money arrival of fellow left-footed defender Josko Gvardiol has since pushed the Spaniard further down the pecking order.
Laporte is now set to embark on a fresh challenge in the Saudi Pro League with Al-Nassr, who are captained by five-time Ballon d'Or winner Cristiano Ronaldo and who have already made a number of notable summer signings including Sadio Mane, Otavio, Marcelo Brozovic, Seko Fofana and Alex Telles.