In 1937, the British Indian government established a temporary air strip at Port Blair for handling fighter aircraft. During the Second World War, British Overseas Airways Corporation (BOAC) operated routes connecting the Indian subcontinent with the Malay peninsula via Burma and Siam. In mid-1941, alternate routes had to be planned due to the advancement of the Japanese forces, which involved flying from Calcutta to Port Blair and onward to Dutch East Indies. In December 1941, the alternate routes were activated after the Japanese invaded Siam, and the Port Blair airport served as a refueling stop for the allied aircraft. After the Japanese captured the Andaman and Nicobar Islands in June 1942, the runway was paved and the air strip was improved to make it capable of handling passenger flights. However, bombings during the war damaged the airport, and made it non-functional.

After the Indian Independence, the Government of India permitted Airways India to operate non-scheduled passenger flights using a Catalina aircraft between Calcutta and Port Blair in 1955. Regular commercial services to the airport were started by the Indian Airlines in 1960. The control of the aircraft operations at the airport was handed over to the Indian Navy in 1984. In 2002, the airport was renamed after Indian ideologue and politician Vinayak Damodar Savarkar. Plans for starting international flights from the airport were proposed in the late 1980s. However, the airport did not see a regular international service until 2024, when Air Asia launched services to Kuala Lumpur, which was discontinued less than a year later.