Drinkwater, 21, is a half-back while Tonga international Vea plays in the back-row.
The Dragons have released Drinkwater from his contract to enable him to make the switch to Super League.
Dragons coach Steve Price said: “Josh has received a good offer and opportunity to play in the Super League and we respect and understand his desires to take up this opportunity. We thank him for his services and contributions to our club and wish him well for his future.”
Vea has previously played in the NRL for Cronulla and Melbourne.
Broncos head coach Tony Rea said: “The squad is delighted to welcome the hard working and skilful attributes that Atelea brings to games.”