Dragons Coach Paul Turner said: "We're delighted to get Marc. We tend to lack a bit of experience and direction and Marc will bring us that.
"He's a knowledgeable guy and he will add to our mix. Australian back-play has always been at the forefront of world rugby and he will help the youngsters here as well."
Stcherbina began his career with New South Wales Waratahs before moving to Biarritz, then to England for a successful spell with Northampton.