The LNG conversion-ready product carriers will be 610ft-long and weigh 50,000dwt, with a 330,000 barrel cargo capacity.
The contract complies with the Jones Act, which requires that ships carrying cargo in the US are to be built in domestic shipyards.
General Dynamics NASSCO vice-president and general manager Kevin Graney said: "Nassco is pleased to continue our commitment as good environmental stewards by building the most energy-efficient tankers in the Jones Act fleet and in helping to sustain and grow highly-skilled jobs right here in San Diego."
The Eco-class tankers have been designed by DSEC , a subsidiary of Daewoo Shipbuilding & Marine Engineering of Busan, South Korea.
According to Nassco , the new Eco design tankers offer enhanced fuel efficiency through the G-series Man Me slow-speed main engine and an effective hull design. Environmental protection features include ballast water treatment system.
The ships will be equipped with dual-fuel-capable auxiliary engines and have provision for accommodating LNG fuel-gas systems in future.
This contract will enable Nassco to add 500 jobs to its existing 3,000 workforce.
The supplies under the deal will close in 2017 with the fifth tanker scheduled to be delivered in the second quarter of that year. The contract for the fifth tanker was signed in June.