"Nothing's difficult about this. I had the greatest time at Manchester City at a great period in their history," said Bellamy to the press as he was paraded by Cardiff City.
"I was bought to take the club (Man City) on to the next stage and I feel I played a big part in doing that. The players they're signing are incredible. The next couple of years I'm sure they'll get the Premier League title, and I hope they do."
Bellamy refused to comment on reports City would not allow him to join a rival Premier League club but praised manager Roberto Mancini.
"There's no ill feeling," added the 31-year-old. "I hope he does well, he's a top manager."
Bellamy explained the chance to spend more time with his family was his primary motivation for joining Cardiff, and he does not expect to have it easy in the second tier.
"My wife and kids live here and I've spent the last six years travelling up and down the road," he said. "I left home at 15. I've always wanted to come back but I wanted to come back at the top of my game.
"I've come down to the Championship willing to put my neck on the line. It's probably the hardest football decision I'll have to make in my career.
"I grew up in this league and it's tough, and that gives me excitement as well. It's a great challenge for me."