The 23-year-old goal-kicking outside back came through the ranks at Warrington, before moving to Bradford, where he racked up close to 300 points in 2015.
“I can’t wait to get over there and get stuck in,” Shaw, who was born in Cumbria, told his new club’s official website.
“We’ve only just finished our season but I’m looking forward to getting cracking again and getting to know the boys.
“In all the games that I’ve watched and even when I played against Rovers earlier this year, the attacking rugby the team plays is really eye-catching and hard to defend against.
“That will suit my game I think so I’ve just got to work hard to prove myself and fit in there somewhere. This year, I’ve played both centre positions, both wings and full back so I’m pretty versatile and happy to play anywhere.
“It’s a strong team so I need to keep my head down, work hard and try to cement my place. I feel I did that this year at Bradford and I’m backing myself to do it again in Super League.”
Rovers head coach Chris Chester believes that Shaw will add quality and competition for places across KR’s back line.
“Ryan is a young player who we have kept an eye on for some time now and he really stood out with a good performance in our Challenge Cup game against Bradford earlier this season,” he said.
“We’ve been monitoring his progress and we’re excited about bringing him into the club and helping him to develop his game over the next few years.
“He’s skilful, he’s blessed with speed and he’s a strong finisher, so there’s plenty of potential there for us to work with and he’s a very good goal kicker too, which is a bonus.
“He’ll add competition for places across the backline and offers some real depth to the squad in those areas, but he’s a level-headed young player who will be working hard to cement a starting place in the team.”