MacAnthony revealed the signing on Twitter, saying the 21-year-old had put pen to paper on a four-year deal.
"Some good news non striker related. Pleased to announce Jack Payne has signed a 4 yr deal with us. Quality acquisition Poshies," MacAnthony tweeted.
"I'm pleased we as a club continue to purchase top quality young league talent which in turn sees FL clubs benefit financially.
"Jack P will only enhance our already strong squad as we work towards competing for league 1 honours."
Payne, who started out as a trainee at Gillingham, made 14 appearances for Peterborough during a loan spell at London Road last season.
He made his debut for Gillingham as a 16-year-old against Chester in October 2008 and went on to make a total of 113 appearances, scoring six goals.