Rolls said the UK Space Agency had offered it 2.9 million pounds ($3.5 million) to help research "how nuclear power could be used to support a future Moon base for astronauts".
"Scientists and engineers at Rolls-Royce are working on the micro-reactor programme to develop technology that will provide power needed for humans to live and work on the Moon," the aerospace company added in a statement.
Rolls forecast its first car-sized reactor would be ready to be sent to the Moon by 2029.
Friday's news comes as US space agency NASA aims to return humans to the Moon in 2025.
It would be the first visit since the historic Apollo missions ended in 1972.
"Nuclear power has the potential to dramatically increase the duration of future lunar missions and their scientific value," Rolls said.
The group, best known for its engines powering Airbus and Boeing aircraft, will work alongside UK universities including Oxford on the space project.
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