Craig Sandercock's side have had a vacant number one shirt ever since Shannon McDonnell chose to move to Hull and teenager Louis Sheriff went to live in Australia.
Eden, rated as one of the Super League's best young talents, on Wednesday signed a three-year deal on the day of his 22nd birthday, with Rovers paying an undisclosed fee for his services.
"It was a pretty big decision for me to leave Huddersfield as I thought I was settled there for the next couple of years," Eden said.
"Everything happened quickly though and now that it's all been done I'm delighted to be a Hull KR player.
"To know that the club came along and really wanted me on board is a great feeling and I'm looking forward to repaying the faith that Craig has shown in me."
Eden made 27 appearances for Huddersfield last season, with his name gaining notoriety when coach Nathan Brown compared him to Billy Slater, the world's best full-back.
He made his debut for the England Knights against Scotland last month and is Rovers' eighth signing for the 2013 season.
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- Craig Sandercock