The 21-year-old Spurs academy product joins the Posh on a three-and-a-half year deal. Coulthirst departs Spurs having made one first-team appearance the North London side. The former England U19 international had five loan spells including a short stint at League One side Wigan Athletic in August.
He told the Peterborough club website: “The manager really demonstrated that he wanted me to sign for the football club and as a player if you feel wanted then it makes the decision easier. Peterborough are a good side, they score lots of goals and I cannot wait to get started.
“It is a tough decision to leave Tottenham because I have been there a really long time, but I feel it is the right time to make the move and I feel this is the right club to be at.”
Peterborough boss Graham Westley will be looking for Coulthirst to replace 23-year-old striker Connor Washington who joined QPR last week.
Westley said: “I think he wants to try to become the next Conor Washington, the next Craig Mackail-Smith, the next Britt Assombalonga and he has all the talent and attributes to fulfil that.
“I am delighted that he has decided that we are the place he wants to join. I used to watch him every week when I was at Stevenage as Tottenham under 21s play their fixtures there and he had phenomenal pace off the shoulder, a great ability to get in behind and an eye for goal.”
Coulthirst had been in great off late for the Spurs U21’s scoring five goals in the past games four including a brace against Chelsea in the U21 Premier League and another brace against Porto in the Premier League International Cup.
Below is footage of that entertaining nine-goal thriller between Spurs and Chelsea which included two goals from the new Peterborough front-man.