The 23-year-old, who had been on trial with Posh, has signed a two-year deal.
Manager Darren Ferguson told the club's website: "We have looked at Frazer, he is a local lad in terms of where he has been playing and we brought him in for a few days so we could take a closer look at him.
"He did very well, we have kept tabs on his progress and I am delighted we have got him into the club."
Blake-Tracy added: "It is a good opportunity for me at a club that has given players from non-league an opportunity before. It is up to me now to work hard and try and take that opportunity."