The versatile forward, 20, made a handful of Super League appearances but wants more game-time.
Cator will get that in the Championship and Leigh head coach John Duffy said: "Joe wants to play games and he's going to come over from Hull, live in Leigh, get a job and get stuck in.
“That's the sort of commitment we want. He's hungry and determined.
"Hull KR have released him from his contract and Joe's going to be a great addition to our squad.
“He is very versatile and can play back row, hooker or middle. He's an outstanding prospect.
"He went to both Coventry and Newcastle last season to get game-time and played some first-team games for Hull KR but he sees this as his big opportunity.”
Cator said: “I played five games for Rovers in 2018 and it's not enough at this stage of my career.
“I realised I needed more game time and I got my manager to get my clips out there. “When John got in touch I didn't need to think twice.
"John's helping me get a job and I'm looking forward to moving over and getting started. “It will make me grow as a person and will be a bit of a reality check for me. It's just the challenge I need and a great opportunity I don't intend to waste."