At a function organised by the university here, Bachchan, 71, presented La Trobe graduate Roshan Kumar.
La Trobe University Vice CHancellor John Dewar said it was an exciting and important day for the university.
"It is both an honour and delight to host the legendary film actor Amitabh Bachchan at the Melbourne campus of the University.
"La Trobe University is very proud that Bachchan has agreed to work with us and help support the education of the next generation of Indian leaders who will help make a difference to the complex problems facing our world today," Dewar said.
He said La Trobe has had a strong link with India since the late 1960s, when then Prime Minister Indira Gandhi visited the campus.
"We have many long-standing connections with India and currently host more than 1,100 students from India. We would welcome more to study here," he said.
Kumar, who originally is from Ranchi, will undertake a PhD into the potential of using social media to better communicate health messages to India's estimated 80 million social media users.
Kumar graduated from La Trobe with a Master of International Business in 2010. He studied a Bachelor of Engineering at the Birla Institute of Technology in Ranchi in 2006.
"I am honoured to receive this scholarship which will help fund my research into improving the health of thousands of people living in India. Social media has immense potential to act as a powerful communication tool to share health information with millions of people," Kumar said.
"I have grown up watching Shri Amitabh Bachchan in movies. To imagine that I would meet him in person still seems like a dream. La Trobe University has certainly provided me with some fantastic opportunities in the past and I am very confident that my future association with the university will be very rewarding for my career," he said.
The scholarship will be presented every four years by Bachchan to an Indian citizen to develop a thesis related to media, digital technology and communication.