Posh boss Mark Cooper told BBC Radio Cambridgeshire: "Jake will give us a bit more bit in midfield, which will certainly give us another option.
"He is a box-to-box midfielder and we are delighted to have him on board."
Livermore also had two spells out on loan last term - at Crewe Alexandra, where he broke his leg in a pre-season friendly, and at Milton Keynes Dons.
Meanwhile, Posh have confirmed that they will spend the next five days training in Tenerife.
Both Livermore and fellow new arrival Reuben Reid will be flying with the squad to Spain.