The Newport back-rower has penned a one-year deal with the regional side after impressing coaches during the pre-season.
Stoddart was drafted in by the Dragons last season and made his regional debut against Edinburgh.
"Hywel is a robust ball-carrying forward who has real physicality and makes a big impact in the collisions," said director of rugby Robert Beale.
"He caught the eye last year but the coaches felt that to take that next step he needed to be in full-time conditioning and I am grateful to Newport for letting him do that. You see talented players week in, week out in the Premiership but the regional environment is totally different and Hywel has already shown that he can thrive in it.
"He has certainly impressed in pre-season and has earned that contract through hard work."
Stoddart has been rewarded for his performances in training and he will provide cover in the back-row for Wales stars Toby
Faletau and Dan Lydiate.
"We've made a conscious decision to run with three frontline second rows and are looking for (back row forwards) Andrew Coombs and Jevon Groves to provide cover there," added Beale.
"We talked about the possibility of recruiting a lock but felt that beefing up our back row was a priority with Dan and Toby (Faletau) sure to be leaving us for international duty.
"If it wasn't Hywel then it would have been someone else coming in but his efforts in pre-season meant that we didn't even consider looking elsewhere.
"He is work in progress, and I am sure he would be the first to admit that. But everything is on a level playing field here and he will be vying for selection in that first game along with everyone else. It's up to him now to earn a contract extension by continuing to impress in training and when given a chance on the pitch, but he certainly has the hunger to succeed."