The versatile centre joins Bernard Jackman’s side following a three-year stint in rugby league.
Wellington made his debut for the Saints at the Magic Weekend in 2016 signed a professional deal with the league giants following his impressive performances during a two-week trial.
He caught the eye of the Saints’ scouts playing rugby union for Aberavon Quins – but has also played the other code for Wales at Under-16 and Under-18 level as well as with the South Wales Scorpions.
Dragons head coach Jackman said: “We want to build a team around young men hungry enough to work hard to help us be successful on and off the field.
“I have some friends in rugby league whose opinion I trust and they tipped me off as to Calvin’s ability. The qualities he brings are pace, power and footwork.
“Every time I met him his desire to come back to Wales and try and make a name for himself in rugby union was infectious.
“So I felt it was worthwhile to negotiate his release from St Helens so that we can get him into our environment immediately and get him upskilled into the technical and tactical areas that are so important in our game.
“All our coaches are looking forward to working with him.”
Wellington could make his debut for the Welsh rugby union debut for the Dragons either at Northampton Saints in the Anglo-Welsh Cup next weekend or in the meeting with the Scarlets at Newport’s Rodney Parade a week later.