Delph initially turned down the move and said last weekend that he would be staying with Villa but he has now signed a five-year deal with City.
The 25-year-old, who has been capped six times by his country, completed his medical on Friday, and will fly out to Australia this weekend to join his new team mates on their pre-season tour.
City triggered the £8m release clause in Delph’s contract last week but the former Leeds man released a statement in which he said: “I’m not leaving.
“I’m staying at the football club and I can’t wait for the start of the Premier League season.”
However, having now opted to make the switch after all, he becomes the second young England international to join City in the space of a few days, following their signing of Raheem Sterling from Liverpool.
Delph said: “Leaving Aston Villa football club is the hardest decision I have ever had to make.
“I have had some amazing times and made great friends during my time at the club. I will always be thankful to them for giving me the opportunity to play in the Premier League.
“As has been widely reported, I initially turned down the opportunity to join Manchester City. That decision was purely down to the love I have for Aston Villa and their great supporters.
“When I was made captain of Villa it was a huge honour for me and I took the responsibility incredibly seriously. I signed a new contract last season with the view of staying at the club for the duration of the deal and never with the intention of leaving a year later.
“My decision to stay initially was purely based on the emotion and feelings that I hold for the club and the people there rather than looking at the football opportunity that had been placed in front of me.
“I have been immensely proud to captain such a great club and want to thank everyone at Aston Villa – most importantly the fans – for the amazing support they have shown me during my time there.
“I am now excited for the future with Manchester City and helping the club to succeed in the coming season and beyond.”
Manchester City manager Manuel Pellegrini told the club’s website: “Fabian Delph is an excellent player and I am looking forward to working with him.
“He has made a huge impact in recent seasons at Aston Villa, and is now one of the brightest young midfielders in the Premier League.
“Fabian has tremendous skill and energy, and the fact that he has become a regular member of the England squad is further evidence of his progress over the past few seasons.
“At just 25 years old, he still has his best years ahead of him.”
Aston Villa said in a statement: “We can confirm that Fabian Delph has exercised the release clause in his contract and will join Manchester City.
“We’d like to wish him success in his future career.”