A three-member committee, headed by Vice President Hamid Ansari, had cleared his name for the post, an official statement said.
Mr Vempati previously worked with Infosys and now heads an online media company.
Information and Broadcasting Minister M Venkaiah Naidu tweeted to congratulate Mr Vempati on his appointment. He hoped that the public broadcaster will scale new heights under his leadership.
Prasar Bharati Chairman A Surya Prakash said Mr Vempati had played an active role in a committee formed to explore the setting up of a digital platform.
An alumnus of IIT-Bombay, Shashi Shekar Vempati has over two decades of experience as a technocrat with specialisation in areas of corporate management, technology consulting and digital media.
He will succeed Rajeev Singh, member (finance) of the board, who was serving as the interim CEO after S C Panda retired earlier this year.
The previous CEO Jawhar Sircar had quit in October last year, a few months before his tenure was due to end, following which Panda, member (personnel), Prasar Bharati, was made the acting CEO.
The committee also consisted of Press Council of India Chairman Justice (Retd) C K Prasad and Information and Broadcasting Secretary Ajay Mittal, who is the President's nominee.
Mr Vempati has been serving as a member (part-time) of the board since February 2016.
He has served in the public broadcaster as chairman of the audit committee, member of the finance and accounts committee, the technology committee, the sports rights committee and the HR committee.
Mr Vempati had worked with Infosys for more than a decade as a product strategist and digital innovator in the US.
He holds two patents relating to real time business event monitoring, tracking and management of inventory of products.
Mr Vempati has also authored several books, including Broadcasting Technologies in India, National Digital Security Architecture in India and Creating a Global Media Platform out of India.
Prasar Bharati, an autonomous body under the Information and Broadcasting Ministry, has All India Radio (AIR) and Doordarshan as its arms.