Thanking Seychellois President Danny Faure for the gift, Prime Minister Narendra Modi said the creatures with long life span have witnessed three centuries and are a symbol of "our ever-lasting" friendship.
"In India, this creature and other animals are seen with a lot of love and compassion," he said in his press statement.
The pair will be kept at Hyderabad Zoo, a Ministry of External Affairs official said.
The giant tortoise, endemic to the east African island nation, weighs around 120 and 150 kg and have the ability to live for up to 200 years.
In 2010, Seychelles had loaned two giant tortoise to Shanghai Zoo in China, while another pair was presented to Guangzhou Zoo in 2014, according to Seychelles News Agency.