The 12,000-water-depth Ocean Rig Skyros will work in West Africa for six years under the deal.
The letter of award came from a major oil company, whose identity DryShips did not reveal.
The total value of the contract implies a day rate of more than $590,000 per day.
The contract, if finalised, will begin before the first quarter of 2015.
George Economou-led DryShips also said that Ocean Rig finalised a five-well deal for the same drillship.
