Clarke-Harris, who turned 18 on Saturday, moves to London Road on a free transfer after leaving Coventry this summer.
Posh boss Darren Ferguson told the club's official website: "Jonson is a young lad who we were made aware of. He actually played against our youth team in a friendly last season and he caught the eye. He has an extremely powerful left-foot, he is big, strong, wants to learn and we think he has a chance.
"It is our gain and Coventry's loss, I have seen him at first hand and we felt it was a bit of a no-brainer for us. For his age, he is physically a man already and has good pace and strength. We just need to teach him how we want to play, but we are happy to have him on board."
Clarke-Harris was a prolific scorer for Coventry's youth team, carried that promise into reserve team football, and became the Sky Blues' youngest ever first-teamer when making his senior bow at the age of 16.