Soward, 31, a former New South Wales State of Origin playmaker, had a spell in Super League with London in 2013.
He returns to the Broncos - where he scored 68 points, including five tries - following his release by National Rugby League side Penrith Panthers.
He had not featured for the Panthers since 4 June and was most recently dropped to the reserve grade side.
St Helens had been linked with Soward, with the Super League side short of cover in the halves with Luke Walsh and Theo Fages currently injured.
The Australian's return to the capital, until the end of the season, comes as a boosts for the Broncos as they look to return to Super League for the first time since their relegation in 2014.
The west London side sit second in the Championship, with four rounds of the regular season remaining.
"It's clear Jamie is a team player and a genuine competitor with a will to win," Broncos head coach Andrew Henderson said.
"His arrival comes at a good time for us as we prepare for the final push in our season. He will inject some enthusiasm and his experience will stand us in good stead for what's to come in the Super 8s."
Soward's move to the Broncos is subject to the approval of his UK visa.
London Broncos have re-signed Australian stand-off Jamie Soward ahead of their Super 8s campaign.