The 30-share BSE benchmark jumped 1,041.47 points or 1.87 per cent to settle at 56,857.79. During the day, it rallied 1,097.9 points or 1.96 per cent to 56,914.22.
The broader NSE Nifty advanced 287.80 points or 1.73 per cent to 16,929.60.
Among the Sensex constituents, Bajaj Finance rallied the most by 10.68 per cent, followed by Bajaj Finserv that jumped 10.14 per cent after encouraging June quarter earnings.
The other gainers were Tata Steel, Kotak Mahindra Bank, IndusInd Bank, Infosys, Tech Mahindra and Nestle.
On the other hand, Bharti Airtel, UltraTech Cement, Dr Reddy’s, ITC and Sun Pharma were the laggards.
In Asia, markets in Seoul, Shanghai and Tokyo ended higher, while Hong Kong settled in the red.
Markets in Europe were trading lower during mid-session deals. The US markets had ended sharply higher on Wednesday.
“Positive cues from global markets following the Fed policy outcome, as well as domestic large caps’ upbeat earnings, drove the market rally. The Fed’s decision was as expected, while their positive comment dismissing the possibility of a recession and hinting at a slower pace of rate hikes in the coming months boosted global sentiments,” said Vinod Nair, Head of Research at Geojit Financial Services.
Meanwhile, international oil benchmark Brent crude climbed 1.36 per cent to USD 108.1 per barrel.
Foreign institutional investors were net sellers in the capital markets as they offloaded shares worth ₹436.81 crore on Wednesday, as per exchange data.