The teenager attacker caught the eye last season - and League One Posh were quick to send scouts along.
The 18-year-old broke into the first team and hit the ground running, scoring against Chesterfield in the FA Trophy before doing the same against Havant & Waterlooville and Hemel Hempstead.
He will go straight into the club’s Under 21 group and their coaches have very high hopes for him.
Kamara said: “I think it can be a bit of a cliché, but the hard work starts now for me, the coaches at Welling said that and it is true, making your debut or scoring your first goal is obviously a great moment, but it is what comes next.
“I am looking forward to coming back for pre-season and trying to impress. I had some great times at Welling, scoring my first goal was something I will never forget, it didn’t feel real. It was great to be at the training ground with my family, they have really helped me and when I told my Mum that I had been offered a deal, she just started screaming!”
Posh Academy Manager Dan Robinson also told the club’s website: “David was brought to our attention by our Academy Head of Recruitment Sam Gaughran. He had been watched numerous times playing for Welling United.
“He was rated as one of the best prospects in Non-League football. As a club, we are always looking for talent at that level so we brought him on trial, he did well with us and off the back of that, we have offered him a contract and he will go into our Under 21s programme as a future prospect.
“David’s attributes align with what we are after in our forward players, he is quick, strong, and athletic. He can finish and can play across the front three. He is predominantly a central striker and we are looking forward to working with him.”