The duo have taken the Pitmen on from long-term owner Steve Price, who has sold the club after 20 years in charge.
The new owners had already appointed FA Trophy-winning Wrexham boss Andy Morrell as they look ahead to next season in the Southern Central Premier.
In a joint statement, Jones and Dando said: “We are absolutely delighted to be able to complete the deal to take over Hednesford Town Football Club – this journey began some time ago and has certainly been an interesting journey to get to his point.
"We cannot thank the support of all the background teams and people enough, all of which have been involved to assist this transitional period. This historical time is much as a credit to them and we are truly grateful to each and every person.
"There is much work ahead of us and of course with the current situation surrounding Covid-19 we have to work around this, as we plan ahead for the future and in particular the 2020/21 season with Andy Morrell, who has already been working hard preparing for the new season.
"We are very excited with regards our future with the Pitmen and we are incredibly focused on achieving the goals we have set out to really maximise the potential of this football club.
"If things were different in the world right now, we would be gearing up for a huge party this evening to celebrate. However, we will instead have to settle with a quiet drink together on a video chat to celebrate and then tomorrow we can get on with the hard work of bringing a football club that the supporters and people of Hednesford can rightly be proud of. The journey is only just beginning."
Jones and Dando also placed on record their thanks to "The team at Residential and Commercial Engineering LTD, the team at Lionheart Security Services LTD, Graham Jones’ family, Hayden Dando’s family, Steve Price & family, Terry McMahon, the Football Association, the Southern League, Gateley’s Solicitors and all of the players, officials and supporters of Hednesford Town Football Club".
They plan to announce a fans' forum to discuss their plans once the government are able to relax social distancing measures because of the coronavirus pandemic.
The duo added: “Please stay safe and we look forward to seeing you all getting behind the Pitmen for the 2020/2021 season ahead, as we move together landmarking 140 years as a club."