The Rs180 billion ($2.4bn) deal marks the end of a lengthy effort to privatise the heavily-indebted flag carrier that according to the government has eaten up Rs1.1 trillion in public money since 2009.
The airline was founded in 1932 with the first flight piloted by Tata's eponymous chairman himself JRD Tata, flying mail and passengers in a single-propeller de Havilland Puss Moth from Karachi to Bombay, as the city was known then.
Tata Air offered a slice of the high life with Bollywood actresses in its adverts and at one point commissioning Spanish surrealist artist Salvador Dali to design its ashtrays.
The airline was nationalised in the 1950s and in the decades that followed the "Maharaja of the Skies" became synonymous with the hopes and ambitions of the newly independent country.
The airline was founded in 1932 and its first flight was between Karachi and Bombay
"Welcome back, Air India," Tata's patriarch chairman emeritus Ratan Tata tweeted on Friday, while admitting it "would take considerable effort to rebuild" the company.
The airline at one time "gained the reputation of being one of the most prestigious airlines in the world. Tatas will have the opportunity of regaining the image and reputation it enjoyed in earlier years", he said.
In the 1990s Air India began to struggle with competition on domestic and international routes from Gulf carriers and no-frills airlines, and the firm started amassing huge losses and debts.
Successive Indian governments tried to privatise the company but its debts and New Delhi's insistence on retaining a stake put off would-be buyers.
Finally, last year Prime Minister Narendra Modi's government, seeking to sell of a raft of state assets, agreed to take bids for the entire company but to retain some of what the airline owes.
Under the deal announced on Friday, Tata will take on around a quarter of Air India's dues of Rs615bn, while the remainder will be transferred to a special-purpose vehicle.
Tata Group, one of India's biggest and oldest companies, employs over 800,000 people in 100 countries.
Founded in 1868 by Jamsetji Tata, the "Father of Indian industry", Tata owns Jaguar Land Rover, software giant TCS, Tata Steel as well as interests in chemicals, hospitality, consumer goods and communications.
Its subsidiaries include 29 listed entities including software giant TCS, Jaguar Land Rover-parent Tata Motors, Tata Steel and others, which have a combined market capitalisation of over $250bn. Buying back India's biggest international airline -- domestically IndiGo is number one -- is part of its ambitious plans.