Bhattacharya will succeed former banker M V Nair, who is stepping down after completing five years with the company, SWIFT India said in a statement.
The company was created to deliver high quality domestic financial messaging services to the Indian financial community.
Bhattacharya said the venture has a huge potential to contribute significantly to the financial community in many domains.
Nair said: "It has been a fulfilling journey with SWIFT India which is a unique venture on many counts. I would like to thank everyone associated in building this venture from scratch."
SWIFT India CEO Kiran Shetty hoped to work closely with the former SBI head.