The company will acquire interest in approximately 1,500 producing wells primarily in the Cleveland, Tonkawa and Marmaton formations.
Over the year ended April, the wells had an average daily net production of approximately 21,500 barrels of oil equivalent per day (boed).
The assets are spread across nearly 250,000 net acres centered in Roger Mills and Ellis counties, Oklahoma.
FourPoint president and CEO George Solich said: "The assets to be acquired include a large base of production which strengthens our cash flow profile in this uncertain commodity price environment.
"The acquired assets will be instrumental in our ongoing efforts to build a world class portfolio of oil and gas assets in the Western Anadarko Basin."
The company plans to finance the acquisition using $619m equity issued to funds managed by GSO Capital Partners and cash from existing credit facilities.
FourPoint COO and executive vice-president Kamil Tazi said: "Anticipating this transaction, Chesapeake halted its development plans and eliminated the active rigs working in this area in the first quarter of 2015.
"As FourPoint assumes operations, we plan to build back up to their previous momentum and continue to reduce drilling and completion costs while maximizing ultimate recoveries."
The transaction is scheduled to be completed in August.
