Following extended consultations with the city council, terms have now been signed and agreed by both parties.
Posh chief executive Bob Symns said in a club statement: "This marks a unique milestone in the history of the football club and will also show a long-term benefit for not only the club but for the local community, its people and the business sector as a whole.
"Whilst the journey to finalise has taken longer than originally predicted, the complex and detailed new lease negotiation and funding challenges have rightly been afforded the necessary time to complete in a professional and sustainable manner."
He added: "The city council have always been honest and precise in its South Bank vision and how the football club could knit together its aspiration for sport, community, education and carbon challenge excellence at London Road. We are almost there."