The 31-year-old right-back will officially complete his move to the Premier League champions on a free transfer following the World Cup as he is a member of the France squad in Brazil.
He has been with Arsenal since July 2007, when he moved from Auxerre for £6million, and made 284 appearances for the Gunners in all competitions.
He will wear the No 3 shirt for City and his first outing in his new colours is likely to be on the club's pre-season tour of the United States.
Sagna, who has picked up 41 caps for France, took to social media on Thursday to bid an emotional farewell to Arsenal.
He wrote: “To be fair, I don’t even know where to start or even how to say it, but I just wanna thank the whole Arsenal FC... a family to me, a club who taught me so much in seven years.
"A club where i had the chance to progress day by day, a club who always gave me his trust whenever I was personally not at my best, a club who change the kid I was to the man I am today, a club where I had the pleasure to give 200 per cent every game.
“I wanna thank the whole staff working at the club, the fans for accepting me so fast, making it smooth for myself and my family, my team-mates which I consider my true friends today and I had a great pleasure learning with them.
“Of course I wanna thank the coach Mr Wenger who believed in me, gave me his trust and clearly changed my life. Now, it’s time for me to move on and one more time THANK YOU.”
Arsenal also released a statement to confirm Sagna's departure from the club.
It read: "An integral part of Arsenal's defence over the past seven seasons, Bacary Sagna brought his time with the Gunners to a fitting close last month when he helped the team win the FA Cup in his final match.
"Everyone at Arsenal Football Club would like to thank Bacary for his fantastic contribution, and wish him all the best for the future."
Sagna's capture is more good news for City, who announced on Thursday evening that defender Aleksandar Kolarov has signed a three-year extension to his contract.
The 28-year-old Serbia international will now remain at the Etihad Stadium until the end of the 2017/18 season if he sees out his new deal.
The left-back, who has made 99 appearances for City since joining them from Lazio in July 2010, is delighted with his fresh terms and is looking forward to more success in the future after winning the Premier League title twice already.
Kolarov told the club’s official website: “I am very happy and very proud of this new contract. I will give to this club probably the best stages of my football career and I am very happy that I continue with this club which feels now like my home."