He takes up a part-time contract combined with a job working with Leeds-based packaging company Marpak.
Shaw scored 47 tries in 81 appearances for the Rovers but is also a talented goal-kicker, one of the most consistent in Super League.
After being released by the Robins, he said: “I have always liked the idea of making the link across to rugby union at some point in my career.
“Having met with the Yorkshire Carnegie coaching staff I knew this would be the right move for me.
“There will be obvious challenges but I am looking forward to it.
“I have been a full-time player since I was 17 but I have reached the age when you need to think about life after rugby and this opportunity with Yorkshire Carnegie is great for me on both fronts.”
Shaw added: “The chance to train in the great facilities at the club and play at Emerald Headingley was a big draw for me.
“I have spoken to head coach Joe Ford and he was great in talking about how I can adapt my game from rugby league to rugby union.
“Joe played league growing up and he was able to put things across to me clearly. “With his help, and the rest of the backroom staff, I am looking forward to the challenge.
“As a goal kicker, I have always appreciated the importance of kicking in rugby union and I am looking forward to developing my game after crossing codes.”
Yorkshire Carnegie managing director Chris Gibson said: “We are delighted to have secured a player of Ryan’s quality for the new season.
“I would like to thank Richard Gibson and Marpak for their continued support of the club and in particularly with their help with Ryan.
“He is a talented player who will add to our group as we look ahead to the new season.”
Carnegie - who entered a CVA in the off-season due to their financial problems - start their season at Nottingham in the Championship Cup on Friday (7.45pm)