Given was supplanted as City's first-choice keeper by Joe Hart last season and the 35-year-old did not want to spend another campaign sitting on the bench.
"I'd met (new Villa manager) Alex (McLeish) a few times before over the past few years and been very impressed with him as a man and he's been a very successful manager as well so when I got the call and knew there was huge interest, I was delighted to follow it up," he said.
"It was a frustrating season at Man City but there's nothing much you can do. The manager made a decision and you've got to respect that and take it on the chin and you have to move on.
"For me it's about playing football. You've got one career and I want to play as much as I can. It was frustrating but I'm not having a go at anyone - that's just how I felt. I've played for most of my career and not to be playing for a season was very tough.
"I've just turned 35 and I'm at a stage in my career where I need to be playing regularly - that was all I was thinking. Manchester City are going to be a big club in world football, not just in the Premier League, so it was a tough decision but for me, it was the right one."
As for his future career, Given looks likely to be joined at Villa Park by a familiar face in former Newcastle team-mate Charles N'Zogbia. The 25-year-old is set to follow the Republic of Ireland international to Villa in a deal, reported to be worth 9.5million, that will be completed once N'Zogbia has undergone a medical.
Given believes the midlands club are signing a much different N'Zogbia to the one he knew at Newcastle and tipped the Frenchman to make a big impact this term following his two-and-a-half-year stint at Wigan.
"To be fair to Charles, I think he had some issues when he was at Newcastle but I think as a person and as a footballer he's grown. People forget how young he was when he was at Newcastle so I think in the last couple of seasons he's shown at Wigan what a great player he is and he's matured off the pitch as well," said Given.
"I'm looking forward to meeting up with him again, I think a lot of Premier League defenders don't like playing against him, he's very quick and direct with the ball. He's more effective in games, he can score goals and create goals for other players as well and it looks like he's got his head down and the bit between his teeth."