"I am very happy with what he has done for me and now he has decided to go somewhere else.
"We wanted to keep him but he wanted a new challenge and we respect that. For our fans, I can say again that we want to achieve a high level so we are looking for players that can help us make that happen."
And chief executive Scott Duxbury confirmed that West Ham had ruled out the Welshman moving to London rivals Tottenham.
"We refused him permission to talk to Tottenham last week and were determined to keep him despite repeated interest from them and Manchester City.
"However, on Friday he again made it clear to the manager and myself that he wanted to move on.
"Late on Sunday night, Gianfranco and I met and he said it was in the best interests to accept the player's request to leave and therefore Manchester City's bid."
Bellamy, who originally wanted to join Spurs, is expected to make his Man City debut at home to Newcastle on 28 January.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.