Andy, surprisingly released by Glasgow at the end of last season, will figure as a No 6 for the Dragons, having also played there.
New Dragons senior coach Paul Turner said: "I knew of Andrew when I was at Bedford in 1998. He was one of two Moseley back row players I was interested in, the other being a certain Peter Buxton (later to join Newport).
"He subsequently moved to lock and moved to Glasgow but on the most recent Australia tour Matt Williams and Todd Blackadder used him as a No 6, which is where we have signed him to play.
"He is a ball carrier and gives us a lineout option and we are delighted to have secured the services of a young international, albeit capped just the once.
"It was a stroke of luck that he became available as he was due to join Narbonne in France but the move fell through."