The 21-year-old midfielder has made over 100 appearances for Gillingham, helping Martin Allen's men into the promotion places in League Two.
Payne, who came through the youth ranks at Priestfield, is highly-rated and has also been watched by a number of other clubs.
Peterborough chairman Darragh MacAnthony tweeted: "Delighted to announce Jack Payne has joined us on loan till end of season with option in place for permanent transfer in the summer!
"Jack is quality young midfielder who we were close to signing last summer. Better late then never. Will compliment our young squad."