Manager Manuel Pellegrini got his man on Sunday night when Demichelis signed on a two-year contract.
The 32-year old Argentinian will be playing under Pellegrini for the third time in his career, the pair having been together previously at River Plate and Malaga.
Demichelis told his new club's website: "I am delighted to have joined City because I am still hungry for success and want to improve."
"I have been in Europe for 11 years now and this was a great chance for me to play in the Premier League with such a big club.
"When there is a change, there is always a process. There's always a period of adjustment you have to go through. Moving from South America to Europe is a big change and you need some time to settle in because everything is new.
"But in my case, I have lived in Europe for many years and I don't think there'll be any problems in adjusting to life here. Now I want to repay the manager's faith in me out on the pitch. I can't wait to get started."