Hodgson, 21, joined from city rivals Hull FC at the end of 2009 and has since made 27 appearances for Rovers.
Head Coach Justin Morgan said: “Josh has a great attitude to developing his game and I think we’ve seen the fruits of that particularly at the start of this campaign where he’s performed very well.
“There’s still plenty of improvement in him and I think that’s the most exciting thing. It’s also why we’re delighted that he’ll be part of the squad for at least another two years.”
Hodgson’s deal includes the option of a third year, and he has set his sights on winning some silverware with the Craven Park club.
He said: “I’ve learnt a lot from the players here and I think I’ve improved quite a lot.
“I’m really looking forward to spending the next few years here.
“It’s a great bunch of lads, a great team, great coaches and I don’t want to leave.
“Everybody wants to win silverware. It’s what you dream of as a kid. We’ll take one step at a time and one round at a time but if we keep doing what we’re doing then I don’t see any reason why we can’t.”