The 30-share BSE Sensex was trading 565.66 points higher at 56,383.77. The broader NSE Nifty jumped 159.85 points to 16,787.85.
From the Sensex pack, Wipro, HCL Technologies, Infosys, Tech Mahindra, Reliance Industries, Bajaj Finserv, TCS and Bajaj Finance were the major gainers.
In contrast, UltraTech Cement, NTPC, Bharti Airtel and Asian Paints were the laggards.
Elsewhere in Asia, markets in Seoul and Tokyo were trading in the green. Trading was closed in China for a holiday.
Stock markets in the US had ended sharply higher on Thursday.
The Sensex jumped 436.94 points or 0.79 per cent to settle at 55,818.11 on Thursday. The Nifty climbed 105.25 points or 0.64 per cent to finish at 16,628.
Meanwhile, international oil benchmark Brent crude declined 0.09 per cent to $117.42 per barrel.
Foreign institutional investors offloaded shares worthRs 451.82 crore on Thursday, according to stock exchange data.