N'Zogbia is now due to discuss personal terms with Villa and then undergo a medical before the deal is complete.
If all goes to plan, N'Zogbia will put pen to paper on a bumper contract until the summer of 2016 and become new Villa boss McLeish's second signing of the summer after the arrival of Shay Given.
Villa said in a statement: "The club are pleased to confirm that we have agreed a fee with Wigan for French international winger Charles N'Zogbia.
"We will now discuss personal terms with the player and arrange a medical, with a view to completing the transfer later this week."
McLeish will hope the deal is done and dusted by the time Villa return from their current tour of Hong Kong this weekend.
McLeish said: "He is an exciting player and someone I've admired for quite a while.
"I'm pleased we've managed to agree a fee and hope we can reach agreement with Charles as soon as possible.
"The deal hasn't been fully done yet, he still has to complete a medical. I believe everything else is just about there," McLeish added during an Asia Trophy press conference in Hong Kong.
"I think it's a great addition to the squad. He's an explosive player and he gives us a little bit of quality to replace one or two of the guys that have left the club.
"We try to do as much homework as possible to ensure we can get it done. You can never say it's a 100 per cent done deal, that's why I remain cautious, but I'm pretty confident.
"You saw his exploits last season, especially towards the end of the campaign when he scored five or six goals which were extremely important for Wigan to stay in the league.
"I felt we needed to replace (Stewart) Downing with similar quality, he's broken into the French national team, I believe we've got a player who can become even better."
Villa skipper Stiliyan Petrov was equally enthusiastic about N'Zogbia's impending arrival.
"He's an exceptional talent, he would be an amazing signing for us," he added.
"He's improved so much in the last couple of years and we'll be glad to have him in our team because he can bring something special.
"He's a very explosive player, he likes to take people on and when you have a player like that, you take a lot of pressure off the team.
"Every time he's faced us, he's torn us apart, he'll be an exciting signing."
It means McLeish is finally set to sign N'Zogbia at the third attempt.
The Scot looked to have landed the services of N'Zogbia 12 months ago when in charge at Birmingham only for the deal to collapse at the 11th hour over personal terms.
Then McLeish's bid to sign the former Newcastle player earlier this summer was halted when Wigan rejected an initial £9million bid from Villa.
McLeish has been keen to bring in a new wide player after the sale of Ashley Young and Stewart Downing to Manchester United and Liverpool, respectively for total fees of around £36m.
N'Zogbia fits the bill and his efforts during the tail end of last season played a major part in Wigan retaining their Premier League status, including scoring a last-gasp winner against West Ham.
He will be reunited with his former Newcastle team-mate Given, who last week became McLeish's first signing of the summer in a £3.5million move from Manchester City.
But the Frenchman will have to wait to meet Villa's first-team squad as he does not have the required work visa to join up with the Hong Kong trip.
He will instead work at Villa's Bodymoor Heath training complex if and when the deal is formally completed.