Obika spent the first half of this campaign at Crystal Palace, where he made eight appearances for the Eagles and he has also had temporary spells with Yeovil and Millwall.
Posh boss Gary Johnson was delighted to capture a player with npower Championship experience and confirmed that he will go straight into the squad for the FA Cup third round tie at Fulham.
Johnson told the club's official website: "He still has a lot of experience to gain but he has played in the Championship and he has scored a lot of goals at this level.
"I have spoken to people within the game who have had him and they rate him highly and we are very pleased to get him on board.
"He is a strong striker, he is not a target man as such, but he is powerful and gets on the end of moves and a type of a player we didn't have in the squad. I am very pleased that everyone has agreed to allow him to sign for us and he goes straight into the squad for the game at Fulham."