The England midfielder signed for Mark Hughes' City side on Tuesday in stark contrast to his protractred on-off move to Liverpool last summer.
Barry, who is in the England squad for this weekend's game against Kazakhstan, agreed a five-year deal worth around £110,000 a week after seeing City's list of summer transfer targets.
His move has spared outrage among Villa fans but Barry's letter, sent to the Birmingham Mail, said: "I feel I am joining a club that will seriously challenge to win major honours, people might doubt that, but I am convinced with the plans the club has short term and long term, and the backing the manager will receive from the owners, that we will be a major force.

"I have honestly been very undecided what to do, the manager and the whole club have bent over backwards to try and persuade me to stay and made me a fantastic offer, which I am extremely grateful for."
Barry stops short of apologising for the move but reveals he believes he was in danger of going stale after 10 years at Villa Park.
The News of the World revealed City's plans on Sunday morning, along with their desire to sign Carlos Tevez, whose loan deal at Manchester United is up.
This article has 3 comments
Fullerson,
I do not believe that Dan "dissed Jamaican people".
But when I read a script like yours. My god. Absolutely terrible. I hope your football is a damned sight better than your spelin. Doh
By Dave. Posted June 6 2009 at 9:46 PM.
dan u need to shut up geezar villa r nt even gud enuf to be in di champo league n u try to diss ppl abt jamaican nobodies..shut up u ediat...fuller tpormented ur crop team at villa park..watch nex season agen..rudolph austin 4 life
By fullerson. Posted June 5 2009 at 12:47 PM.
Good scoop, but as a villa fan, could you give us some hope and give us a nice scoop in return? who are we interested in other than Jamaican no bodies!
By Dan. Posted June 3 2009 at 1:43 PM.