The 35-year-old prop had been on a month’s trial at the club, and has played three games for them during that time.
London head coach Andrew Henderson is pleaed to have added further reinforcement to his squad.
“I’ve been happy with the contributions that Jamie has made in the three games he’s played during his initial trial with us,” he said.
“He’s brought much needed Championship experience to the squad and will continue to work alongside our younger players helping with their development.”
Thackray himself is keen to keep improving on his recent displays in a Broncos jersey.
“I’ve been happy with how I’ve been training and how I’ve performed in games,” he said.
“Because I’ve obviously missed out on pre-season training I’ve only been back training for three weeks, and now I’ve got three games under my belt, so all I want to do is keep training hard and keep getting that bit fitter each week and keep improving.
“Hopefully some of my experience can rub off on some of the younger players.
“We have some outstanding props coming through and if I can just teach them a little bit of what I’ve been through that’ll really help with their development.”