The missile will be capable of launching from an attack submarine or a US Navy surface warship, and will have a shorter range than the ballistic missiles stored on Trident submarines or on land.
The project previously faced opposition from the Biden administration, which requested to defund the programme in the last defence budget.
The administration argued that the role of sea-launched nuclear cruise missiles could be fulfilled with existing weapons, and that the warheads alone would cost $31 billion (£24 billion).
Republican congressmen launched an attempt to retain the project and successfully added it back into the budget passed in March.
American public spending rules require the government to spend money in the way Congress demands.
The construction of the new missile follows plans for some Western countries to bring nuclear weapons out of storage.
Nato ‘will remain a nuclear alliance’
In an interview with The Telegraph on Monday, Jens Stoltenberg, the secretary general of Nato, said member states “need to consult on these issues”.
“Nato’s aim is, of course, a world without nuclear weapons. But as long as nuclear weapons exist we will remain a nuclear alliance, because a world where Russia, China and North Korea have nuclear weapons, and Nato does not, is a more dangerous world,” he said.
The decision to award a contract to begin research and development on a sea-launched cruise missile comes after lengthy debate on Capitol Hill about the merits of the project.
In 2022, Admiral Charles Richard, then responsible for the Pentagon’s nuclear weapons command, said that the missile was “necessary to enhance deterrence and assurance.”
“The current situation in Ukraine, and China’s nuclear trajectory, have further convinced me that a deterrence and assurance gap exists,” he said.
One possible use for the missile would be in a future conflict in the Taiwan Strait, where Xi Jinping has instructed the Chinese military to be prepared for a ground invasion by 2027.
China has one of the fastest-growing nuclear stockpiles in the world and is thought to be developing more “tactical” nuclear weapons to be deployed on the battlefield without sparking a full-scale nuclear war.
The Stockholm International Peace Research Institute, a Swedish think tank, warned on Sunday that China’s stockpile of ballistic missiles could eclipse the United States and Russia by 2030.