Goal reported on Tuesday that City had agreed a £4 million deal with Atleti for the former Argentina centre-back, while Manuel Pellegrini admitted on Saturday that he expected "progress" on the deal over the weekend.
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"I am delighted to have joined City because I am still hungry for success and want to improve," Demichelis told the club's official website.
"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."City moved to sign the Argentine following injury to Vincent Kompany, though Matija Nastasic returned from the sidelines for Saturday's 2-0 victory over Hull City Tigers.