The Abergavenny born fly-half will link up with Worcester with immediate effect.
The 26-year-old has made 66 appearances for the Dragons since his debut in 2013 and will join the English side as they look to finish their Aviva Premiership campaign on a high.
Dragons Head Coach, Bernard Jackman commented: “This is a great opportunity for Dorian to get some regular rugby and we would like to wish him all the best for the remainder of the season.”
