The 30-year-old, who had 12 months remaining on his contract at Headingley Carnegie, had been linked with a string of NRL clubs.
"I've achieved a lot of things at Leeds over a 14-year period but I'm ready for a new challenge at Hull KR," Bailey told Hull's official website.
"It was a difficult decision to leave Leeds, I was born in the city and I've won some great finals with the club but now I want to bring some of that experience to Rovers. It's going to be a big challenge but I'm looking forward to it and I'll be meeting it head on.
"The fans are really passionate and hopefully we can breed a winning culture and start getting to finals. We've got some really ambitious players who want to win things here at Hull KR and hopefully I can add to that and bring a bit of grunt up front."
Bailey, a former England and Great Britain international, won six Grand Finals, three World Club Challenge titles and one Challenge Cup during his time with Leeds.