The 21-year-old will stay on loan at Peterborough until the end of the season.
Posh boss Gary Johnson said: “I have seen Kieran play a couple of times and have watched endless DVDs of him.
“He is only a young lad but he is talented, can score goals and we like his energy and work-rate.
“We think he is ready and mature enough to play at this level and he comes very well recommended by David Moyes.”
