The appointment is effective from February 16, 2012, following formal approval from the Board of Vodafone India.
Singh, a leading industry figure, is the founder and chairman of Max India as well as its subsidiaries like Max New York Life Insurance Company, Max Healthcare Institute and Max Bupa Health Insurance Company.
"Analjit has been a long-standing, reliable and trustworthy partner in India," Vodafone group chief executive officer Vittorio Colao said.
Nick Read, CEO of Vodafone's Africa, West Asia and Asia Pacific region, said: "Singh knows our business well, having been the founder and chairman of Max Telecom, the business which has grown to become Vodafone India with nearly 150 million customers."
Sachin might be rested but will rotation work for India?
Pak's support for terror in India could lead to N-exchange: US
Here's how SC ruling will impact telecom sector
Yuvraj has cancer, undergoing chemotherapy in US
'India, Pak bilateral trade may touch $10 bn by 2015'