Diamond Offshore has also got from Hyundai a fixed-price option to buy a third drillship.
The company plans to name the two new drillships as Ocean BlackHawk and Ocean BlackHornet.
The drillships will have a seven ram blow-out preventer, dual activity capability, five mud pumps and a maximum hook-load capacity of 1,250 tonnes, and will be designed for operations in up to 12,000ft of water.
Diamond Offshore president and CEO Larry Dickerson said the company has purchased, ordered or upgraded seven units with capabilities in 10,000ft of water over the last four years.
"When completed, the new drillship will bring to sixteen the total number of deepwater rigs deployed by Diamond Offshore as we strive to provide returns consistent with our long history of value creation for the Company and our stockholders," Dickerson said.