The 23-year-old France international is City's sixth signing of the summer, following the capture of Bacary Sagna, Willy Caballero, Bruno Zuculini, Frank Lampard and Mangala's former Porto team-mate Fernando.
The centre-back told Manchester City's official website: “City is a top club in Europe. For me, it was an important step to leave Porto and join Manchester City in order to continue my progress.
"I want to win titles and I believe I can do this. I am ambitious and this is why I am here.
“I’m very happy to come to England because, for me, the Premier League is the best league in the world.
"It is a very intense and very aggressive competition. There are plenty of goals, so it is also really nice to watch and I can’t wait to get started.
“The fact that Fernando is here is better because I played with him at Porto but there is also other players that I know like Sagna, (Gael) Clichy and (Samir) Nasri."
City boss Manuel Pellegrini added: “I’m delighted to have added a player of Eliaquim’s quality in the squad ahead of the new season.
“He is already a fine player but in my opinion, he has all of the mental, physical, technical and tactical attributes to become one of Europe’s very best defenders.
“Eliaquim is a player I believe will make an immediate impact in the Premier League, thanks to his physicality, his reading of the game and quality on the ball.
“I think he will prove to be a great signing for us.”
Mangala made 92 appearances for Porto after joining from Belgian club Standard Liege in August 2011 and won the Portuguese title twice with the club in 2011/12 and 2012/13.