The 28-year-old made 100 appearances for Ebbw Vale and played in last season's Principality Premiership win over Pontypridd.
Sweet is a product of the Newport Gwent Dragons academy and has represented Wales at Under-20 level.
"It will be an honour to contribute to a successful Dragons side in the future," Sweet said.
"I began my journey as part of the academy system and playing alongside the U16s all of the way through to the U20s and I have never given up on playing professionally for my home region."
Sweet also featured for the Newport Gwent Dragons Premiership Select squad in last season's British and Irish Cup.
Ebbw Vale lock Ashley Sweet has joined Newport Gwent Dragons on a one-year contract.