The regulator - the US Food and Drug Administration - said its decision was a "historic" moment and medicine was now "entering a new frontier".
The company Novartis is charging $475,000 (£367,000) for the "living drug" therapy, which leaves 83% of people free of a type of blood cancer.
Doctors in the UK said the announcement was an exciting step forward.
The living drug is tailor-made to each patient, unlike conventional therapies such as surgery or chemotherapy.
It is called CAR-T and is made by extracting white blood cells from the patient's blood.