Thompson has been released by Leigh Centurions who are trimming their squad after looking set to miss out of a place in the Qualifiers.
The 26-year-old made 71 Super League appearances for igers from 2009-2013 and another 96 during a four-season spell with Hull.
Rhinos’ director of rugby, Kevin Sinfield said: “He has been a standout player in the Championship this season and has been someone we have been following closely for the last couple of weeks.
“We believe he will be a huge addition to our squad, until at least the end of the season.”
Thompson added: “I am very pleased to sign for the Rhinos.
“It’s not often you get big clubs wanting you and there are none much bigger than this club so I’m ready to just rip in.
“I’ve got a chance until the end of the year to prove myself and I am looking forward to that.
“I’m looking forward to the challenge, I’m here to do a job so I can’t wait for Friday’s game.”