Ginnelly leaves Barwell after eight years and he replaces Lee Fowler, who took over from Nicky Eaden last month.
Born in the town, the manager says he is up for the challenge of saving his local club.
Nuneaton are six points from safety in the National League North. They travel to Darlington on Saturday for his first game at the helm.
Ginnelly, 55, said on the club’s wesbite: “I’m delighted to have this opportunity to manage my home town club. I’ve had success with Stockingford, Atherstone and Barwell and the time is right to try and do the same at the Boro.. I’m looking forward to the challenge.
“I thoroughly enjoyed my time at Barwell and would like to thank the club and fans for their support over the years.
“I’d like to think I’ve left them in a strong position, it’s such a well run club and I thank chairman Dave Laing for his understanding and allowing me to follow through this opportunity.”
Chairman Nick Hawkins added: "He has a proven record of over-achieving and a hard working mentality to create success.
"Hopefully this will be the change in fortunes on the pitch that we need. There's no denying this will be a popular appointment with the fans and, as I've stressed throughout, we are in this together.
"Jimmy and his team, which will be announced shortly, have a huge task on there hands to keep us in the division, but it's one I think we can achieve. I know he will put everything into this, as will the rest of the staff and myself. Let’s get behind the Boro', the new regime and the town."