Ilkeston FC were last month wound-up in the High Court, but Hardy has completed a deal from liquidators Smith Cooper.
Ex-Nottingham Forest defender Steve Chettle has been appointed as manager.
"Ilkeston Town will have its own corporate governance, with separate directors, financial structure and accountability," Hardy told the Notts website.
The Derbyshire club will play in the Midland Football League Division One as Ilkeston Town from next season, five levels below the Football League, with Hardy insisting there would be no conflict of interest.
He added: "Naturally, as would be the case between any professional and semi-professional football clubs, there will be an opportunity for transactions when it comes to such things as the loaning of players, sharing of expertise and so on.
"However, it is essential that any dealings between the two clubs are carried out with the best interests of their respective stakeholders in mind."
Ilkeston Town, then a Conference North club, folded in 2010 owing £50,000 to HM Revenue and Customs (HMRC).
The new club, Ilkeston FC, were admitted into the Northern Premier League Division One South for the 2011-12 season, playing at the same 3,029-capacity New Manor Ground as their predecessors.
But financial troubles overshadowed their season in 2016-17, culminating in them being wound-up.
Notts County owner Alan Hardy has bought non-league side Ilkeston FC for an undisclosed fee.