The Dragons confirmed the news on their official website, with Williams signing a two-year contract in order to return to Wales for the 2018-19 season.
The 24-year-old, who has made three senior appearances for Wales, admits a desire to become a regular for his country was one of the big reasons why he's decided to leave Bristol at the end of the campaign, although he insists he will be giving his all for them until his exit.
He said: "I'm delighted to be coming home to Wales to sign for the Dragons. The vision set out by the Dragons board excites me and I look forward to playing my part in the future of the Region.
"I make no secret of the fact that I have a burning ambition to represent my country again but I also know that I'll need to work incredibly hard at regional level to get there."
He added: "I would like to say a big thanks to Pat Lam and the coaching team at Bristol Rugby for giving me the opportunity to play for the club and I will leave the club a better player than when I arrived. It goes without saying that I will give it my all for the rest of the season to try and help the team gain promotion back to the Premiership."
Dragons head coach Bernard Jackman is pleased with the future acquisition as Williams will be back in Wales following a five-year spell at Scarlets between 2011-16.
He said: "I am delighted to get a player of Rhodri's quality to commit to the Dragons. He is really ambitious and committed to working hard and to reaching his goals.
"I feel that he will be an influential figure for us both on and off the field."