Hodgson, 24, has penned a two-year deal Down Under with the Robins receiving a substantial, undisclosed transfer fee for the England Knights international, who has more than 100 Super League appearances under his belt.
He said: “This opportunity has come at the right time for me and it’s full credit to Hull KR for allowing the move to happen. It’s an exciting time in my career and I’m looking forward to getting across to Canberra next season.
“Hull KR took a chance on me five years ago when I first came to the club and I was grateful for that. I’ve always done my best to repay the faith they showed in me and it was a really tough decision to leave.
“I’ve always had an ambition to play in the NRL and I felt I would have had regrets later in my career if I didn’t take this opportunity.”
Hodgson, who joined the club from city rivals Hull FC in 2010, was under contract for the next two years, and Rovers will have first refusal on his services should he decide to make a return to Super League in the future.
Chairman Neil Hudgell said: “Whilst we are disappointed to lose a player of Josh’s calibre, we fully understand his reasons for wanting to test himself in the NRL.
“As you would expect from Josh, he has been honest with the club from the start of these discussions and we have secured a substantial fee from Canberra as well as agreeing first refusal on Josh if he comes back to the UK.
“He has been a dedicated and consistent professional during his time at the club and we wish him well.”