The 28-year-old Frenchman is now in talks with Boro over personal terms.
City confirmed the news tonight on the club's official website.
Earlier today Andreas Isaksson completed a £2m move from French club Rennes, signing a 3-year deal.
The 24-year-old Swedish number one has won 42 caps for his country and is 6ft 6in.
Isaksson told the City website: "It's a great club to come to, and to come to England and play for a club like Manchester City is an honour for me. It's a big club, there a lot of good players in the squad and I am really looking forward to playing here.
"I feel good, I have been in training for 3 or 4 weeks and it should not take too much time to adjust to playing here," he added. "I think it's more physical for keepers over here and tougher than in France. I am looking forward to that, I think it will suit me.”