The acquisition is the second largest by an Indian company since Tata Steel's $13.6-billion acquisition of Anglo-Dutch steel maker Corus.
Media reports from Kuwait said, "The last big hurdle has been cleared and officials of Zain confirmed the development on Wednesday, Mar 24."
The approval has come ahead of the Mar 25 deadline for an agreement between the two firms.
The deal paves the way for one of the largest telecom cross-border deals which will give Bharti access to 15 African countries at one go.
On being contacted the Bharti spokesperson declined to comment and said, "The company will not comment on any development at the moment."