Thimpson spent time with Rochdale on loan last season, where he played 12 games, and will be available for Peterborough for their next Championship match at Blackpool.
"Josh is a good size and has a lot of potential," Darren Ferguson told Posh's official website.
"We had a look at him before he joined Celtic and I am delighted to now get him on board for the rest of the season.
"We now have four centre-backs and that competition for places is what I was after. I hope that is the first of a couple of signings before the end of the month."