The 20-year-old has been training with Posh this week and, after completing the necessary paperwork and receiving international clearance, goes straight into Darren Ferguson's squad for Friday's night's clash with Walsall.
"I am hoping to get a good run in the team and help the team push for promotion.
"I have been on loan at Brentford, but my chances were limited there. I didn't play as much as I would have liked to down to a few things, but I have moved on and hopefully I can prove a point and do well for Peterborough."
Ferguson added: "Ben is an out-and-out defender. He can play with the ball at his feet, but he loves defending and I think we needed that kind of player.
"He has trained well this week and we are delighted to have him at the football club."