Jones, whose contract expires in June, has kept one clean sheet in 22 games this season.
"Paul is a very highly rated goalkeeper," Posh boss Darren Ferguson told the club website.
"He is a good age, and is out of contract in the summer so this is a good opportunity to get him in."
He's not going to come here to sit on the bench.... we have that Collis bloke for that, he's used to it
SuperPosh7
The move could make way for Posh's first-choice shot stopper Joe Lewis to leave London Road.
The 23-year-old is on the transfer list and is looking to join a bigger club, but Ferguson has insisted Jones will provide back-up to the former England Under-21 star.
"He will provide competition to Joe Lewis which I think he needs," he said.
"The signing does not mean that Joe will be leaving, I just feel he needs a bit of competition."
Source: BBC Sport
Source: BBC Sport