"We have started test flights today. Commercial flights are set to start next week," an Air India official said on Wednesday, declining to be named, adding that international flights may start by the third week of May.
World regulators grounded all 50 operating Dreamliners after a fire aboard a parked Japan Airlines 787 in January and a smoking battery that forced the emergency landing of an All Nippon Airways 787 the same month.
The FAA approved Boeing's new battery system design last month, which allowed airlines around the world to begin modifying the Dreamliner planes.
On Tuesday, India's directorate general of civil aviation gave the go-ahead to the planes after a joint meeting of officials from Air India and Dreamliner-maker Boeing.
"We have allowed them to fly," the DGCA chief Arun Mishra told AFP, adding that he was "satisfied" with the technical reports and modifications made in the jet's battery systems, which were initially identified as a concern.
Air India bought 27 Dreamliners as part of a multi-billion-dollar deal in 2005. It received the first plane last September and now has six, with the remaining 21 due to arrive by 2016.
Boeing has insisted that its Dreamliners are safe.