Jones, 49, won many plaudits for his work in making the Exiles such a strong proposition during their maiden Aviva Premiership campaign, although they were ultimately relegated.
The ex-Ospreys boss was known to be keen to return to Wales, and he takes over a Dragons outfit who have consistently languished near the bottom of the RaboDirect Pro12 table.
They have also seen key players such as Luke Charteris, Aled Brew and Dan Lydiate leave in big-money moves to French clubs over the last couple of seasons.
Darren Edwards will remain as head coach at the Gwent region, with Robert Beale moving from the rugby director role to team manager.
Assistant coach Rob Appleyard has left the Rodney Parade side by mutual consent.
Dragons chairman Martyn Hazell said: "Last season was a difficult one for us at the region, but having brought our finances under control, we are looking to build our team for the future.
"With some key signings made during the off-season, we are confident that Lyn has the experience and expertise to support our coaching team and ensure that we get the very best out of our group of young, talented players."
Chief executive Chris Brown added: "Having stabilised the business and now strengthened the rugby, we believed we have a sustainable product that will secure the future of rugby at Rodney Parade for years to come."