Williams joins from English Championship side Bristol for the start of the 2018-19 campaign and will offer head coach Bernard Jackman versatility at either full-back, wing or fly-half.
The former Wales Under-20 international made 55 appearances for the Scarlets prior to joining Bristol, but is now heading back over the Severn Bridge to return to the regional game
“We’re delighted to bring Jordan back to Welsh rugby and to the Dragons – he’s an exciting young full-back with all the attacking attributes to get people on their feet,” said Jackman.
“Jordan is a talented young player, he’s a quick, elusive runner and is dangerous in broken play.
“At 24, he is still a young man with time to further develop his skills, but we’re confident he will be an exciting addition to our back division who will thrive in the brand of rugby we’re developing at the Dragons.”
Williams added: “I’m excited to be joining the Dragons next season. I’ve enjoyed my time at Bristol, but it’s time for a new challenge and I’m looking forward to playing in Wales again and working with Bernard.
“The Dragons have lots of talented young Welsh players and as a player you get a sense that something exciting is building there, so I can’t wait to get started next season.”
While Williams joins his namesake Rhodri and Wales and British & Irish Lions star Ross Moriarty in joining the Dragons for next season, Jackman has also penned Griffiths to a new contract.
The tough-tackling flanker has captained the Dragons in recent weeks after returning from injury and won his first senior Wales cap against Tonga last summer.
“I enjoy going to work every day,” said Griffiths. “The culture within the group is great and it’s the best feeling to play alongside your best mates.
“I am very passionate about playing for my home region having grown up in Gwent and I have seen vast improvements since the takeover.
“I feel the Dragons is the best place for me to progress in my rugby career and the support we have from coaches, medical team, analysts and the Welsh Rugby Union is great.
“It is only going to help me progress further.
“I believe the future is positive for the Dragons with everything in place in order to allow us to achieve our goals. Everyone involved is extremely ambitious and committed to working hard to become a very successful region.”
On Griffiths’ contract extension, Jackman added: “Ollie is one of the brightest back-row talents in Wales. He won his first senior cap in June and I expect him to gain many more in the future.
“He is a leader on and off the field in our group and we are over the moon that he has signed a long-term deal to stay in his region.”