The Australian, 40, has spent the last four years at Rovers in various coaching capacities including a spell as head coach following Chris Chester’s exit in 2016.
He was then made Tim Sheens’ assistant and carried on that role when Tony Smith arrived in June.
However, with Featherstone head coach Ryan Carr reported to be imminently heading back to Australia, Webster - who has also worked as Wakefield Trinity head coach and France assistant - is set to take control at Post Office Road for 2020.
“I have enjoyed working with all of the players, coaching staff and supporters of the club,” said Webster, who played almost 100 games as a scrum-half for Rovers, captaining them to promotion in 2006.
“The two head coaches, in Tim and Tony, that I have worked with have taught me a lot both personally and in furthering my knowledge of the game.
“I am indebted to their time and support. I felt that it was the correct time for myself to pursue a new challenge which I am looking forward to.
“I will always deep-down support this club and will be back next year when possible to take in some games.
“I wish everyone including the board, players and supporters the best of luck for 2020.”
Smith added: “I had and still have a great relationship with James, we remain close and always will be.
“We’re in regular contact and I’m very grateful for the short time that I have spent with him.
“He has been fantastic for me, and terrific in terms of his knowledge and coaching ability. He’s been incredibly supportive, loyal and honest towards me and I know he’s very passionate about Hull KR.
“But I also understand that he wants to further his career as a head coach and feels that other opportunities have come up for him in that respect.
“It was with some regret and reluctance that James has left but at the same time it was the right thing for the progress of his career.”