Griffiths has agreed a deal to make the move to Rodney Parade and will link up with his new team-mates at Ystrad Mynach from Monday.
The hard-running and powerful centre – who stands 6ft 2in tall and weighs 102kg – joined the Saracens Academy in 2015 before stepping up to the senior squad in 2017.
The 23-year-old made his debut in the English Premiership last season and helped Saracens Storm win the Premiership Rugby Shield.
“It’s an exciting time for me to join the Dragons,” said Griffiths.
“I’ve spoken with Dean Ryan and the things he has said are really positive. I feel the potential here is phenomenal so hopefully good things are to come.
“There are some fantastic players here too so I’m looking forward to developing my game and taking the chance I have been given.”
Welsh-qualified Griffiths – who has also spent time on loan at Bedford Blues and London Scottish – joins fellow new recruits Sam Davies and Jack Cosgrove at the region.
Dean Ryan, Director of Dragons Rugby, said: “Tom is a talented young centre who has spent the last four seasons working on his game in the Saracens set-up and also getting valuable game time on loan at London Scottish and Bedford Blues.
“He is keen to now really prove himself, take on a new challenge, and excited by the opportunity at Dragons.
“We’re excited to see how Tom develops in our environment and look forward to him linking up with the squad.”