Robson, who had made 23 appearances for the region and scored 92 points over the last four seasons, has agreed a new deal to remain at Rodney Parade.
“Arwel is a young fly half who really wants to play for this region,” said Dean Ryan, Director of Dragons Rugby.
“He still has lots to learn and now needs to play regularly and show he can develop in our environment.”
Caerphilly-born Robson made his regional debut for Dragons in November 2016 against Leicester Tigers in the Anglo-Welsh Cup.
The 23-year-old joins fellow backs Rhodri Williams, Tavis Knoyle, Josh Lewis, Jordan Williams, Will Talbot-Davies, Owen Jenkins and Rio Dyer in putting pen to paper on new terms.
“I’m really happy to sign for my home region and excited for the future here,” said Robson.
“I really feel we’re building something special at the Dragons, which is underlined by the progress we’ve made this season, and I’m determined to play a big part in that journey going forward.”
Robson is a former Wales Under 18 and U20 international who spent part of the 2019/20 season on loan at Jersey Reds.