Posh boss Gary Johnson told the club's official website: "He still has a lot of experience to gain, but he has played at this level and scored goals.
Obika goes straight into the squad for Saturday's FA Cup tie at Fulham.
He has made just two appearances for Spurs, both in the UEFA Cup two seasons ago, when he came on as a late substitute in Nijmegen in November 2008 before starting against Shakhtar Donetsk three months later.
Source: BBC Sport
Source: BBC Sport