The 22-year-old moves to London Road as he is out of contract with the Chairboys, although Wycombe are entitled to compensation.
"It is a really good signing for the club and I am delighted to have him on board," the Posh boss Darren Ferguson.
"As soon as I knew he was available we were able to complete the deal very quickly.
"The lad has a great attitude, he wanted to come to us despite having two Championship clubs in for him and that is because he knows what direction the club are going in."