Dragons head coach Darren Edwards has said that he hopes Burton's influence will boost his side for next season.
"Any team that has played against Kris knows how influential he can be on a game with his goal-kicking and tactical awareness," PA quotes Edwards as saying.
"Alongside the recruitment of Richie Rees, we now have a good blend of young and experienced half-backs.
"It gives us the opportunity to generate competition and allows us to create combinations that can be influential and exciting for the team."
Burton has 21 Italy Test caps.