Taylor, who came through the Club’s Academy, has made 24 first-team appearances since his debut in 2014 and was part of the Warriors side which lifted the B&I Cup trophy in 2015.
Warriors Director of Rugby Alan Solomons said: “Huw is at the stage of his career where he wants to get regular game time and he now has an opportunity to move to Dragons and work hard to get that.
“We thank him for the professionalism he has shown during his time at Sixways and wish him the best of luck in the next chapter of his career.”
Taylor said: “I have thoroughly enjoyed my time at Sixways and have made some lifelong friends along the way.
“I would like to thank the Academy coaches, first-team coaches and my teammates for their support over the last few years and wish the Club well in the future.”