The highly-rated forward has agreed a three-year deal at London Road.
Gordon, who has already been given a taste of first-team action by Posh manager Darren Ferguson, is currently the leading marksman with the club's reserve side.
"I am obviously very happy to sign my first professional contract and I realise that the hard work really begins now," Gordon told the club's official website.
"I have enjoyed training with the first team and it was fantastic to come on against Wolverhampton Wanderers earlier in the season. I am very grateful for the opportunity and I aim to seize it with both hands."
Ferguson added: "We are delighted he has signed. He has a good future ahead of him and turning professional will be a day he will always remember. He has been a part of the squad, both last season and this season, and we have high hopes for him."
- Sports & Recreation
- Darren Ferguson