The Premier League asked for more time to ratify the deal despite Villa starting to submit the relevant documents before 4pm on Tuesday - an hour before the transfer window formally closed.
But Villa were always confident Dunne would become their player after passing a medical and agreeing a four-year contract, and he has now officially ended his nine-season spell at City.
The Football Association were also satisfied with the paperwork presented by Villa but needed the approval of the Premier League.
Dunne becomes Villa's second defensive capture after Welsh international James Collins signed from West Ham on Tuesday for £5million.
Martin O'Neill has been desperate to bolster his back four after skipper Martin Laursen retired and Zat Knight was sold to Bolton.
He said: "Richard Dunne is the kind of person we are looking for."
Dunne's days at Eastlands appeared to be numbered after the arrival of Kolo Toure from Arsenal and then Joleon Lescott from Everton.
Villa started the current campaign with only two experienced centre-backs in Curtis Davies and Carlos Cuellar.
The need for new blood became even more pressing after Davies started to suffer more regular recurrences of his long standing shoulder problem and he may need surgery.
O'Neill was forced to blood 19-year-old Ciaran Clark alongside Cuellar in Sunday's 2-0 home success over Fulham.
Villa agreed a fee last week with City for Dunne but the deal dragged on past the weekend because the player wanted to sort out financial issues relating to the remaining three years of his contract.
Dunne would have been entitled to a testimonial next summer when he would have completed a decade of service at City.
Villa skipper Stiliyan Petrov said: "He's the captain of Ireland, he's been the captain of Manchester City. You love to see players like that coming to this club.
"Martin Laursen was a big player for us, with his presence and his influence. But he, like Gareth Barry, is now gone and we need to get on without him.
"The arrival of Dunne will help us to do that."
Villa had previously splashed out £29million since the end of last season on Stewart Downing (£12million), Stephen Warnock (£8million), Fabian Delph (£6million) and Habib Beye (£3million).