The 23-year old central defender was a target for Manuel Pellegrini in the January transfer window but they could not get the deal done.
However, having returned to negotiations at the end of the season City have now secured their sixth signing of the summer and Mangala will link up with Brazilian midfielder Fernando, whom the club signed from Porto in June.
"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," Mangala told mcfc.co.uk.
"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 are also other players that I know like (Bacary) Sagna, (Gael) Clichy and (Samir) Nasri."
In addition to Mangala Pellegrini has already brought in full-back Sagna, goalkeeper Willy Caballero, midfielders Fernando, Frank Lampard (on loan) and Bruno Zuculini.
Having been beaten 3-0 by Arsenal in Sunday's Community Shield the Chilean stressed the need to have greater competition for places and Mangala's arrival certainly gives him that in defence.
"I'm delighted to have added a player of Eliaquim's quality in the squad ahead of the new season," said Pellegrini.
"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."