Briggs will officially become a Posh player for the next month when the transfer window for loan deals reopens at midnight on Tuesday.
The 20 year-old will go straight into manager Darren Ferguson's squad for the visit of npower Championship leaders West Ham on Saturday.
"Matthew is a lad I have been interested in for a while, even when I was at Preston," Ferguson told his club's official website. "He is a good size, has great pace and has a good left foot and I am delighted to bring him here.
"He can play at centre-back but his main position is left-back. He will strengthen us, without a shadow of a doubt. He gives us another option and he adds a bit of quality to the squad."