Officials from both nations signed a "declaration of principles" to deploy the equipment, making Singapore the first Southeast Asian country to install the specialised technology in cooperation with the United States.
Singapore, the world's busiest port last year in terms of shipping tonnage, is a vital link in Washington's battle to prevent terrorists from smuggling components for nuclear weapons and "dirty bombs" into the United States.
The agreement is part of the US National Nuclear Security Administration's "megaports initiative" aimed at detecting and intercepting illegal shipments of nuclear weapons materials before they reach US ports.
"The United States and Singapore both recognize the need to remain vigilant against the threat posed by the trafficking of nuclear and other radioactive materials," said US ambassador Frank Lavin, who signed the accord for his government.
Lock Wai Han, the commissioner of Singapore's Immigration and Checkpoints Authority (ICA), said the city-state's participation demonstrated its commitment to helping safeguard maritime security and the global trading system.
"Being an international maritime hub, Singapore views the enhancement of homeland and (shipping) container security as an important response to the threats posed by terrorism," he said.
An ICA spokesman said the radiation equipment was expected to be installed and operational within six months.
Thursday's agreement compliments another effort by the US Homeland Security Department called the container security initiative in which containerized cargo bound for the United States are inspected by US customs officers at their points of origin.
US officials began inspecting US-bound cargo in Singapore two years ago.
Singapore is one of the United States's staunchest allies in Asia in the war against terror.