Fairfax will pay Rs 2,149 crore ($322.75 million) for the stake, GVK said in a statement to the stock exchange.
The deal, likely to be completed by mid-2016, will help GVK reduce debt by Rs 2,000 crore and save up to Rs 300 crore a year in interest costs, the company said.
"This is an important and successful milestone in deleveraging our balance sheet, and all proceeds from this stake sale shall be used to bring down our debt obligations to our lender," company chairman and managing director G V K Reddy said.
Shares in GVK, which also operates Mumbai airport, ended 6 per cent higher. The Mumbai market fell 1.46 per cent.
Fairfax, headed by well-known contrarian investor Prem Watsa, made billions by correctly calling the 2008 financial crisis. In 2014, the Toronto-based company set up Fairfax India to boost the firm's investment in the country.
Fairfax India went public in 2015 and raised more than $1 billion via its initial public offering.
($1 = Rs 66.5850)
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.