The 19-year-old is linking up with Posh for a second time, having starred for the London Road club in League One and the Emirates FA Cup last season.
Peterborough manager Grant McCann stated: “It is great to have Martin back at the club.
“He is well-loved by the players and the staff and of course the supporters, I am sure he will bring a lot more quality to us and we are looking forward to working with him again.
“George has returned to Barnsley. They are similar players, but Martin can play in numerous positions for us whereas George could only really play in one. It is great to have that quality in the squad."