The Spaniard completed a move to Russia from the Premier League champions on Thursday, putting pen to paper on a five-year deal.
After making 76 appearances in all competitions in two seasons at City, the arrivals of Frank Lampard and Fernando at the Etihad Stadium had brought Garcia's place as a regular starter into question.
Upon his arrival, the 27-year-old told Zenit's official website how Villas-Boas had persuaded him to join the club.
"I spoke with Villas-Boas several times and he was one of the main reasons why I came here," he said.
"He's very enthusiastic about the project because he believes we can do great things here.
"Now it is finalised I am very happy to be part of this incredible team and I am willing to begin to help the team as soon as possible.
"I had the opportunity to speak with [former Benfica team-mate Ezequiel Garay]. I was told the club and the city was incredible and that it was a very good opportunity."
