Das and Shahani are among 16 World Fellows selected in 2014 from a pool of about 4,000 applicants.
With the addition of Das and Shahani, the global Yale World Fellows network now includes 15 Indian Fellows, more than any other country since the programme was established in 2002.
The 2014 group also includes an Italian robotics engineer and artist, a Pakistani environmental lawyer, a Syrian peace activist and a 2012 candidate for President of Iceland.
This year's cohort brings the total number of Yale World Fellows since the programme's inception in 2002 to 257 Fellows, representing 83 countries.
"It is a privilege to welcome these impressive leaders to campus," said Yale President Peter Salovey.
"Like prior cohorts, the 2014 Yale World Fellows are dynamic, high impact practitioners committed to effecting positive change. Das and Shahani fit that mold perfectly and will bring immense talent and vision to the group," said Yale World Fellows Director Michael Cappello, professor of pediatrics at the Yale School of Medicine.
"Through the Fellowship, Yale will provide these global leaders the valuable opportunity to take a step back from the intensity of their work and to develop a strategic vision for their personal and professional trajectories and continued impact on the world," he said.
According to a statement, from August to December, the 2014 World Fellows will participate in specially designed seminars in leadership, management, and global affairs taught by leading Yale faculty; audit any of the 3,000 courses offered at the University; engage in discussion and debate with a wide range of distinguished guest speakers.
The Yale said Nandita Das is an award-winning actress and director who has leveraged her international profile to campaign on social issues including child mortality, gender and race issues and violence against women.
She was the first Indian to be inducted into the International Women's Forum Hall of Fame for her contributions to the arts and in 2013, she supported the Dark is Beautiful campaign, an effort draw attention to the unjust effects of skin colour bias in India, it added.
Parmesh Shahani heads the Godrej India Culture Lab, an experimental ideas space in Mumbai at the intersection of academia, business and creative industries.
He is also Editor-at-Large for Verve Magazine, India and the author of Gay Bombay: Globalisation, Love and (Be)Longing in Contemporary India.
Thirteen previous Yale World Fellows hailed from India:
Abhik Sen, Managing Editor, The Economist Group
Prodyut Bora, National Executive Member, Bharatiya Janata Party
Unmesh Brahme, India Country Director, Room to Read
Subhashini Chandran, CEO, Woodbriar Group
Ayush Chauhan, Managing Director, Quicksand
Celine DCruz, Coordinator, Slum Dwellers International
Paromita Goswami, Founder, Elgar Pratishthan and Shramik Elgar
Monika Halan, Editor, Mint Money
Sonali Kochhar, Clinical Research and Drug Development Specialist, PATH
Nachiket Mor, Director, Board of IKP Center for Technologies
Chetna Gala Sinha, Chair, Mann Deshi Mahila Group
Amit Wanchoo, Managing Director, Eaton Laboratories
Ruchi Yadav, Senior Program Officer, The Hunger Project