The 24-year-old ex-England Under-21 man joined the Royals from Watford in 2015 and has made 14 first-team appearances.
But he failed to play for the Berkshire club last season, with his only senior football coming in an eight-game loan spell at Gillingham.
Posh had been in talks with Tottenham over keeper Luke McGee, who spent last season on loan at the ABAX Stadium.
"Jonathan has good experience, he has played in the Championship with Watford and was part of the side that got promoted with them," said Posh manager Grant McCann.
"He is being coached well by David Beasant at Reading and we are pleased that they have allowed him to come here for six months.
"If all works well then hopefully we can extend it in January."
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League One side Peterborough have signed goalkeeper Jonathan Bond on a six-month loan from Reading.