BREAKING: Three Welsh internationals are returning to Wales
Williams will join fellow Bristolians Jordan Williams and Ryan Bevington.
The 24-year-old will return to Wales and the Guinness Pro14 championship at the end of this season.
The scrum-half has made 27 appearances for Bristol and has also made three appearances for Wales since his debut versus Tonga in 2013.
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.”
Wales’ new Senior Player Selection Policy, which is similar to that used in Australia, came into effect last month.
Under the changes, those playing their domestic rugby outside Wales will now be available for the national team providing they have won 60 caps or more.
WRU chief executive Martyn Phillips said: “We have decided to make these changes to protect the ‘investment’ made by Welsh rugby – by our coaches, supporters, clubs, communities and fellow team members – in those individuals who rise to the top and make it to international rugby.
“We have established a clear incentive for those players approaching the prime of their rugby playing careers to stay in Wales and it is now there in black and white for everyone to see.
“The revamped policy will be reviewed periodically but, fundamentally, if you have less than 60 caps and you leave Wales then you won’t be selected by your country again until you return.”
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