It is part of vast divestment plans unveiled by the US natural gas giant.
"Royal Dutch Shell plc today said it acquired acreage in Texas from Chesapeake Energy in a further step to build a leading portfolio of shale assets rich in oil and natural gas liquids," Shell said in a statement, adding the deal would close within 30 days.
"This announcement supports Shell s strategy of further building an industry-leading liquids-rich shale resource. The acquisition provides both existing production and near-term growth potential from a proven resource, as well as promising opportunities for expansion.
"The acquisition covers 618,000 net acres in the Permian Basin in West Texas that currently produces some 26,000 barrels of oil equivalent per day and has significant growth potential."