The contract has a value of around $550 million, and includes four one-year extension options, Maersk said in a statement.
The jack-up rig, which is currently under construction in Singapore, is to be used for drilling the wells on the Hild field development, an exploration project led by the Norwegian unit of French energy major Total S.A. (TOT).
The contract is expected to commence by the third quarter of 2014 at the latest, Maersk said.
Maersk's ultra harsh environment jack-up rigs are designed to operate in conditions found in the North Sea; it already has two in operation, and another two are being constructed.