The government has sold the airline to the company, which was the highest bidder at nearly $2.4bn (£1.7bn).
The Tata group originally founded the airline in 1932 before it was taken over by the government in 1953.
The government had for years been trying to sell the airline, which has racked up losses worth $9.5bn.
But it recently sweetened the deal by making the terms of the debt less onerous for the buyer. It's still unclear how much debt the Tata group will take on under the new terms.
Air India has many assets, including prized slots at London's Heathrow airport, a fleet of more than 130 planes and thousands of trained pilots and crew.
Tata Sons already run two airlines in India - Vistara, a full service carrier in partnership with Singapore Airlines, and AirAsia India, a budget airline in partnership with Malaysia AirAsiaBhd.