The 25-year-old half-back came through the ranks at Wigan, before joining Warrington at the age of 16.
He also played for South Wales Crusaders and Keighley before he joined Batley.
“I’m really excited to be joining the Broncos, it’s obviously a big move for me moving away from my family and friends but I’m really looking forward to a new challenge,” Leatherbarrow told the Broncos’ official website.
“Training full time will benefit my game in a number of ways. Obviously you get the little things such as better recovery but also you spend more time around your team mates, more time on the field doing core skills and specific training around set positions. I believe that will all really help.
“My aim for 2016 is to improve myself as a half-back and become a better player. As a team we want to be challenging the top four and get into the qualifiers and challenge to get back into Super League.
“Moving to a full-time environment made my mind up about the move straight away. Trying a new lifestyle, away from my comfort zone and training full time.
“Also speaking to Andrew Henderson, he really came across well and I believe he will really improve me as a player. It was a no brainier really.”
Broncos head coach Andrew Hendersonis hoping that Leatherbarrow can thrive in London’s full-time environment next year.
“Scott came through the Wigan system and when opportunities were limited there he’s taken his chance elsewhere,” he said.
“He’s embracing the opportunity to get back into a full time environment with the Broncos and kick on with his career. He’s really buying in to what we’re building here.
“Scott has a good kicking game and is a great organiser so he can get the team around the field. I’m looking forward to working with Scott to build him up as a player and add more qualities to his game to really bring out the best in him.”