Investor sentiment improved on hopes that gradual lifting of lockdowns across the world would help start economic recovery, traders said.
After surging 783.07 points during the day, the 30-share BSE index ended 605.64 points or 1.89 per cent higher at 32,720.16.
Similarly, the NSE Nifty advanced 172.45 points, or 1.84 per cent, to close at 9,553.35.
HDFC was the top gainer in the Sensex pack, rallying over 7 per cent, followed by HCL Tech, M&M, HDFC Bank, Tata Steel, SBI, Bajaj Finance and Infosys.
On the other hand, Axis Bank, Asian Paints, HUL, Titan and IndusInd Bank were among the laggards.
Indian markets opened on positive note taking positive cues from its Asian peers and ahead of U S Federal Reserve's decision on interest rates amid ongoing coronavirus pandemic, said Narendra Solanki, Head- Equity Research (Fundamental), Anand Rathi.
"Indian benchmarks extended their gains in late afternoon session as traders also took encouragement from reports of Finance Minister's likely announcement of larger stimulus package for the economy, which also led to some short covering in heavily negative sectors like financials ahead of monthly expiry on Thursday," he said.
Bourses in Shanghai, Hong Kong and Seoul settled on a positive note. Markets in Europe were also trading higher in early deals.
International oil benchmark Brent crude futures rose 2.99 per cent to USD 23.41 per barrel.
On the currency front, the rupee surged 52 paise to provisionally close at 75.66 against the US dollar.
Meanwhile, global tally of coronavirus infections has crossed 31 lakh, with over 2.17 lakh deaths.
The death toll due to COVID-19 in India rose to 1,007 and the number of cases climbed to 31,332, according to the health ministry.
