The company had acquired a 49 per cent stake in WBSPL in May 2012 for USD 165 million.
At that price, the additional stake purchase would have cost Airtel an estimated USD 165 million, or Rs 1,008.1 crore at today's exchange rate.
However, the company did not disclose the financial details of the deal.
In a statement, Airtel said that it has "completed the acquisition of 100 per cent equity shares of Wireless Business Services Private Limited, which holds BWA Spectrum in the Indian telecom circles of Mumbai, Delhi, Haryana and Kerala".
Airtel acquired a majority stake in WBSPL in July by increasing its stake to 51 per cent from 49 per cent.
WBSPL has spectrum that can be used for high-speed 4G services in New Delhi, Mumbai, Haryana and Kerala. Airtel has the similar spectrum in Punjab, Maharashtra, Kolkata and Karnataka.
Airtel has already launched 4G services in Bangalore, Pune, Kolkata, Chandigarh, Mohali and Panchkula.
Shares of Airtel were trading at Rs 353.80, up by 1.46 per cent, in the afternoon session at BSE today.