The 23-year-old defensive midfielder has signed a five-and-a-half-year contract, with the Potters paying Porto a fee of £18.3million.
City Chief Executive Tony Scholes said: "Giannelli is a player we have been trailing for some time and we are delighted to have concluded a deal to sign him.
"At one stage it looked unlikely that we would be able to get the deal over the line but things accelerated quickly earlier today and Giannelli is really excited about the prospect of playing in the Premier League with us."
Manager Mark Hughes added: "Giannelli is a good young player. He has great power, good ability on the ball and a great range of passing and there's no doubt he will add to the quality that we already have at the Club.
"He played against us in pre-season and although I was already aware of him, seeing him at first hand resonated with me."
Imbula launched his career with Guingamp in 2009 and four years later joined Marseille where he got his first taste of Champions League football.
Porto paid Marseille €20m for his services last summer and soon afterwards he lined-up against the Potters in the Colonia Cup in Germany.