The statues were unveiled prior to the Premier League champions’ 5-0 win over Arsenal on Saturday.
Kompany and Silva played pivotal roles in helping establish Man City as a major English and European force.
Kompany joined Man City from Hamburg in 2008 and starred for eleven seasons in the blue half of Manchester, making 323 appearances and captaining the side to four Premier League titles, two FA Cups and four League Cups.
"I didn't really expect to be recognised by such a great club in that way," Kompany told the club's website.
"My wife is from Manchester, my kids are born in Manchester, and they go back to a place where they can see something that represents what their dad has achieved and that is something that I can't describe.
"The first time I saw the statue I couldn't believe how big it was, but then again, I'm a big boy, so fair enough! And then especially the pose, for me it means a lot."
City signed Silva from Valencia in the summer of 2011, with the Spain world cup winner making 436 appearances for the club and winning four Premier League titles, two FA Cups and five League Cups.
"Being at City changed my life. I'm proud of what we did together and I feel emotional that it has been recognised like this," said Silva, who now plays for Real Sociedad.
"When I first saw the statue, I felt good, I thought it was like me. This statue really represents the way I like to play, I love the pose the sculptor has chosen.
"It really reminds me of those times I was on the pitch playing and that moment when I had to find the striker."
Another Man City great, Sergio Aguero, is next in line to get a statue outside the Etihad.
