The 25-year-old French winger put pen to paper on a five-year deal after passing a medical on Thursday evening.
"I am really happy and extremely excited to sign for Aston Villa," N'Zogbia told the club's official 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 can't wait to meet my new teammates, play with them and work together to do something special this season."
N'Zogbia joined Wigan in 2009 from Newcastle United for a fee of £6m.