Swaraj said it was a matter of pride for her to inaugurate the academic session of the university after a gap of over 800 years.
"I am really upbeat that I got this opportunity...," she said at an event held in the Buddhist pilgrim town of Rajgir in Nalanda district, about 100 km from here.
The university will be built in Rajgir, 12 km from where the ancient Nalanda University stood till the 12th century.
Bihar Chief Minister Jitan Ram Manjhi also accompanied her. Senior Bharatiya Janata Party (BJP) leader and former deputy chief minister Sushil Kumar Modi was also present.
However, former Bihar chief minister Nitish Kumar, who played a major role in setting up the university, was not invited, university officials said.
According to the university Vice Chancellor Gopa Sabhrawal, ambassadors of Singapore, Thailand and representatives of other countries involved in setting up the university were present at the function.
Classes at the varsity started Sep 1 with 15 students and half-a-dozen faculty members.
The fully-residential university, to be completed by 2020, will have seven schools, all for post-graduate and doctoral students, offering courses in science, philosophy, spirituality and social sciences.