The deal brings Bharti 42 million new subscribers and an estimated annual revenue of $3.6bn in a business that made losses for the first nine months of 2009.
Bharti will pay $9bn in cash and assume $1.7bn debt from Zain, putting the deal value at $10.7bn in what the Indian media have dubbed Bharti's "African safari".
Zain, which said it will make a net profit of $3.3bn from the sale of its African assets, however, saw its biggest share drop in two weeks on Wednesday.
"The main challenge for Bharti lies in raising revenues and adding subscribers, as Zain has been losing both in some of the countries," Amit Ahire, an Indian investment analyst, said.
The trick for Bharti, which pioneered low-cost telecoms in India, will be to bring down Zain's high cost base and get subscribers to talk more using lower tariffs.
"A big challenge is streamlining operations across all these countries with limited resource availability," Kamlesh Bhatia, another analyst said.
Obstacles in Africa
The government of Gabon has come out against the deal, saying Zain Gabon had not complied with regulations, and it reserved the right to take "all necessary measures".
There is also a dispute about minority ownership of Zain's operations in Nigeria, the biggest market in the deal.
Several lawsuits are being heard in Nigerian, British and Dutch courts on the Nigeria issue, according to a BNP Paribas report.
Bharti would also talk to shareholders in Zain Nigeria, Mittal, ranked eighth on Forbes' list of Indian billionaires, said.
Mittal appointed Manoj Kohli, head of Bharti's international operation, to oversee the African business on Wednesday.
Kohli helped build Bharti into India's leading mobile operator by subscribers with more than 125 million subscribers.
In building Bharti, Mittal is credited with helping transform India from a country where people paid bribes for phones and faced huge bills into a place where almost everyone has mobiles and call costs are the lowest in the world.
The number of people owning phones in the countries where Zain operates stands at just 32 out of every 100 compared with India's 51.
This is the second largest foreign takeover in Indian corporate history, after Tata Steel's $13 billion buy of Corus in 2007.
"We are excited at the growth opportunities in Africa," Mittal, who twice failed with bids for South Africa's mobile giant MTN, said.
"Africa is a continent of hope and opportunity."