The Tata group and Singapore Airlines joint venture began operations with its maiden flight from Delhi to Mumbai.
Singapore-based BOC Aviation's Managing Director and Chief Executive Officer Robert Martin said it would deliver three more aircraft by end of March this year.
It has already delivered two planes to Vistara.
By March 2016, BOC Aviation would have delivered a total of 13 aircraft to the new carrier, Martin said.
All the planes would be Airbus-320s.
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Vistara, the launch of which also marks the re-entry of Tatas into the Indian aviation space after more than six decades, plans to operate 87 flights in the first year.
Vistara would operate 148-seater Airbus A320-200 with 16 seats in business class, 36 in premium economy and 96 in economy.
Overall, Vistara will be the third full-service carrier in the country, after state-run Air India and private carrier Jet Airways.