The transaction, expected to be completed by mid-2016, would also help the diversified entity save around Rs 300 crore annually on interest costs.
Bangalore International Airport Ltd (BIAL) owns and operates the Kempegowda International Airport Bengaluru. The airport started operations in May 2008.
In BIAL, GVK Group holds 43 per cent stake, Siemens Project Ventures GmbH 26 per cent and Flughafen Zurich AG Ltd 5 per cent while state-owned entities Airport Authority of India and Karnataka State Industrial Investment & Development Corporation Limited hold 13 per cent each.
"Upon completion of this transaction, there would be reduction of debt burden of around Rs 2,000 crore and would also result in savings of interest costs to the extent of Rs 300 crore per annum," the company said in a release.
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Grappling with substantial debt burden, GVK Power has been exploring avenues, including possible IPO of its airport business, to raise funds.
GVK Airport Developers, a wholly-owned subsidiary of GVK Power, had initiated a financing process last year to reduce its debt obligations.
"All proceeds from this stake sale shall be used to bring down our debt obligations to our lenders.
"We chose Fairfax as a partner in BIAL as we have a long standing relationship with its chairman, Prem Watsa and we would look forward to partnering with them in developing Kempegowda International Airport through its next stage of expansion as we develop a new world-class Terminal 2 and a new runway," Reddy said.
The transaction is subject to customary closing conditions and third party approvals including lender consents, and is expected to be completed by mid-2016.
"GVK shall remain a long term investor and pioneer in airport assets in India. GVK is bullish on the airport sector in India and shall continue to build iconic assets for the country," it added.
Fairfax India's Chairman Prem Watsa said it would work closely with all stakeholders to manage the stake in BIAL going forward.
G V Sanjay Reddy to continue to lead the management team as Managing Director (MD) of BIAL and G V K Reddy would remain as Co Chairman, he added.