The 19-year-old has been playing for Hull’s reserve team and has made two first-team appearances.
“I was offered a chance to stay at Hull FC but I decided to go Rovers because I think I’ll have an opportunity to play more first-team rugby,” said Hodgson.
“It’s been a really tough decision and an emotional one and at Hull they’ve got a lot of good young hookers and a lot of good back rowers as well, so I think there’s more chance of breaking into the first team at Rovers.”
Rovers boss Justin Morgan said he expected Hodgson to be a success at Craven Park.
“I’ve been keeping an eye on Josh for a number of years now”, said the coach. “I think he’s developed over the last couple of years and I think he’ll add substantially to our squad.”
Morgan added: “He’s got the desire to be part of a team that’s going to be pushing for trophies and we expect him to have a long Super League career in a red and white jersey.”