The 18-year-old scored 11 tries for the Rhinos' 2022 Grand Final-winning team and has stepped up to the reserves this season.
Tchamambe crossed for a hat-trick in England colours in an academy win over France in July.
"It's an honour signing for Hull KR," he said.
"There's a huge buzz surrounding the club at the moment, especially with all the new signings that are coming in, and I'm really excited to join the same environment as these players.
"Seeing how the club has improved over the past few years is incredible and I can't wait to be part of the progress.
"My main focus is my personal development as a rugby player and gaining experience in a first-team environment, learning from the older and experienced players.
"Hopefully through that I'm able to grab a first-team debut and solidify myself as a first-team Super League player."
Tchamambe caught the eye of Rovers boss Willie Peters representing Yorkshire against Lancashire at Craven Park earlier this year.
"He's a big body and finds his front when he's carrying the ball," said Peters. "He has some real speed when he gets going.
"We're confident Neil can apply himself and develop into a Super League player here at Hull KR."