The 24-year-old left back has been granted a work permit and passed a medical but will not join City on their pre-season trip to New York, the club said on its website.
"I have watched him a lot since then (2007) and so have the Manchester City scouts. His attacking capability is very good. He is fast and can shoot with power and accuracy," City's Italian boss Roberto Mancini told the club website.
"He also has the ability to play in numerous positions and is very good in midfield. This is an additional benefit to the team. He has a fantastic international career ahead of him. I am looking forward to working with him."
British media have reported Kolarov has signed a five-year contract and leaves Serie A side Lazio for a fee of £19 million.
The versatile left-sided player, who joined Lazio in 2007, joins new signings David Silva, Yaya Toure and Jerome Boateng at Eastlands ahead of the new season and takes their spending to a reported £75 million.
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