Bellamy, who joined West Ham for �7.5m last season, has previously had spells at Norwich, Coventry, Newcastle, Celtic, Blackburn and Liverpool.
He has now been reunited with boss Mark Hughes, who managed him with Wales and at Blackburn.
"Mark was a big factor in my decision because he has always pushed me really hard," said Bellamy.
"He knows how much I enjoy training and that I need to be tested at the highest level."
Bellamy, who was unveiled on Tuesday along with Dutch international midfielder Nigel de Jong, is expected to make his Man City debut at home to former club Newcastle on Wednesday night.
And he believes struggling City can reverse their fortunes and climb into the top half of the table.
"The project here is going to be phenomenal," said Bellamy.
"We are going to be competing right at the top and I still think the top six is realistic this season.
"Throughout my whole career I have always been involved in the top six. That is what I am aiming for here."
John Hartson, a former team-mate, earlier said he believes City have made a shrewd purchase in Bellamy.
"I know he's moved around a lot and let himself down on occasions, he'd be the first to admit that," Hartson told BBC Radio 5 Live.
"But he is very good professional, the first on the training ground and the last off it."
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