The 26-year-old has signed a two year and a half deal, keeping him in England until at least the end of 2021.
“It is great to get the deal sorted and I am looking forward to getting started with Leeds,” Martin told the Rhinos’ official website.
“The move has come about very quickly. I came close to signing for Leeds last year but opted to stay at the Bulldogs. The club have kept me in their plans and I am pleased things have now worked out.
“I know the team are in a tough position at the moment but I want to come over and hopefully play my part in getting Leeds back where we want to be.”
During his time with Canterbury, Martin played 25 games and scored four tries.
After granting Martin his release, Bulldogs CEO Andrew Hill spoke on the subject.
“Rhyse is an excellent young man and when he came seeking a release from his contract yesterday to take up a longer deal in Super League we decided not to stand in his way,” he said to bulldogs.com.au.
“We had previously offered Rhyse a contract extension, but he felt that moving to Super League was the right decision for himself and his career and as such we have agreed to allow him to leave before the July deadline.”