The Welsh club have announced that Beard had agreed a two-year contract.
The 25-year-old, who qualifies to play for Wales, has made 41 appearances for Edinburgh since joining from New Zealand side Bay of Plenty in 2013 and has scored two tries.
Beard said: “It was a hard decision to make, but I am really looking forward to the new challenge that lies ahead. The chance to try something new was a great opportunity for me, one which I couldn’t give up.
“I have spoken at length to the coaching staff at the Dragons and they have all spoken highly about what the club are looking to achieve going forward.
“The Dragons have improved immeasurably and are a very happy team.
“I have enjoyed my time with Edinburgh and would like to thank the coaches, staff and players who have all been supportive since I joined the club.”
Lyn Jones, the Dragons director of rugby, added: “Sam has played exceptionally well for Edinburgh and starred against us. He’s a player that gets things right.
“He has a great skill set and is a talented individual and we look forward to him joining the region.”
Edinburgh head coach Alan Solomons said: “Sam has been a valuable squad member over the past three seasons. He is a first-class bloke and a good team man. We wish him all the best in his new challenge.”