The Spain playmaker, who signed from Valencia in July 2010, said City's ambition was behind his decision to agree the deal.
"The team is growing and we are now aiming at the Champions League and so that also is another reason to want to stay here and try and win it," he told the club's website.
City begin their second tilt at glory in Europe's top club competition when they face nine-times champions Real Madrid at the Bernabeu on Tuesday.
"I feel very comfortable here and I want to try and win trophies like those," added the 26-year-old Silva, a vital cog in Spain's Euro 2008 and 2012 victories and the 2010 World Cup triumph.
"These last two years have gone very well so let's hope the next five go as well or even better. The fans have always given me their support since I arrived here and recently they've been wanting me to sign.
"Hopefully this goes some way to thanking them for the affection they've shown towards me, something which also helped me decide to put pen to paper. Being here really does feel just like home for me," added Silva.
Team-mates Joe Hart and captain Vincent Kompany have also pledged their long-term futures to City, the England goalkeeper agreeing a five-year contract extension in August 2011 while the Belgian defender signed a six-year deal in July.
