Eight of them are set to arrive in August from Namibia, home to one of the world's largest populations of the wild cat.
Their return comes decades after India's indigenous population was declared officially extinct in 1952.
The world's fastest land animal, the cheetah can reach speeds of 70 miles (113km) an hour.
Classified as a vulnerable species under the International Union for Conservation of Nature Red List of Threatened Species, only around 7,000 are left in the wild worldwide.
Officials announced the agreement after spending the past two years working on how to transport the animals after India's supreme court decided in 2020 that they could be reintroduced in a "carefully chosen location".