Williams returns to Wales
The 24-year-old joins Dragons from Premiership club, Bristol Rugby.
He will return to Wales and the PRO14 championship at the end of this season.
Williams will join fellow Bristol players, Jordan Williams and Ryan Bevington.
The scrumhalf has made 27 appearances for Bristol and has also made three appearances for Wales since his debut versus Tonga in 2013.
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Dragons Head Coach, Bernard Jackman added: "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,"
The 24-year-old added: "It has been a difficult decision to leave Bristol Rugby, but it’s been massive for me to have the support of Pat Lam and the club throughout the process.
"My time at Bristol has been really enjoyable and it’s a tight-knit group of players who are all working towards the same goal. Obviously, I have international ambitions with Wales and I’m eager to fulfil them.
"For the remainder of the season, however, I’m absolutely committed to Bristol and helping the team achieve promotion,"
