Scrum half Leadbeater (22) picked up 5 appearances for the Dragons last season and has acquitted himself well in several high-pressure matches.
"We're delighted to have Steffan on board for another 2 years," said Dragons Director of Rugby Robert Beale. "He has shown how talented he is and we are looking forward to seeing him develop further with us.
"James is another regional talent who we believe has a bright future in regional rugby. It is again indicative of the direction the region is taking that we are concentrating on developing local youngsters as we see them as being key to the future of rugby at the Dragons."