The 21-year-old scrum-half made his Super League debut in 2012 against London.
“Gilmore is a player that Widnes coach Denis Betts recommended as someone that can get us around the park,” said Broncos head coach Joey Grima.
“Gilmore has a sound kicking game and has played Super League level in 2014. We look forward to welcoming him to the squad.”
Widnes coach Denis Betts was pleased that Gimore would be getting the opportunity to play some first-team rugby.
“I would like to thank Joe Grima for offering Tom a great opportunity,” he said.
“He’s a talented lad and he deserves now to be starting week in week out.
“With the strength of our squad in his position, it means that there are limited opportunities for Tom at the moment but we want to develop him so it’s great that he can get some decent game time with London.
“Again we would like to thank London Broncos for this opportunity for Tom to go there and play some high quality rugby under some good coaching structures.”
Meanwhile, the Broncos will be without Joe Keyes for their trip to Leigh this weekend. He suffered concussion last week against Sheffield and is expected to be absent for at least a fortnight.
Nick Slyney is also likely to be absent, as he is awaiting scans on the injury which forced him out of the action at Sheffield.
Richie Mathers has been cleared to play, however.