Smith, a 20-year-old half-back or hooker, has been released from the final season of his contract after 25 appearances for Warrington Wolves.
Warrington chief executive Karl Fitzpatrick said: “Due to our recruitment and retention for 2019 Morgan would have found his playing opportunities limited.
“Therefore, we felt it was best for Morgan’s development to allow him to explore alternative options. Morgan has been the consummate professional during his time at Warrington and moves on with our best wishes.”
The Normanton Knights product could make his competitive debut for London against Wakefield Trinity in Super League round one on Sunday, February 3.
Broncos coach Danny Ward said: “Morgan is an exciting, young British half-back who already brings with him Super League experience.
“He has come through the system at a top club and we are looking forward to working with him and continuing his development.”
Smith added: “I am very excited to be given such a great opportunity.
“I know I am a young player, but I will be looking to force my way into the team. I can’t wait to get started.”