McLeish had come close to signing N'Zogbia last year when he was in charge at Birmingham, only for the deal to fall through at the 11th hour when the 25-year-old opted to stay with the Latics.
The Scot tried again following his move to Villa in pre-season, but was rebuffed as Wigan fought to hold onto their prize asset.
However, an offer of around ?£9.5 million ($15.6 million) persuaded Wigan to sell and Villa confirmed on Friday that N'Zogbia had signed a five-year contract after passing a medical.
The former Newcastle player will be available to feature for the first time in Wednesday's pre-season friendly against Derby at Pride Park.
"I am really happy and extremely excited to sign for Aston Villa," N'Zogbia told Villa's website
"It is a great club and it is a really big step for me in my career, so I am sure I will enjoy my football here.
"I think it is going to be a really good season and hopefully I'll do well here.
"I can't wait to meet my new team-mates, play with them and work together to do something special this season.
"Alex McLeish is a strong manager and I think he is going to build a really good team for this season."
Source: AFP
Source: AFP