After touching a high of 34,022.01, the 30-share index was trading 725.86 points, or 2.18 per cent, higher at 33,954.66.
Similarly, NSE Nifty surged 201.10 points, or 2.05 per cent, to 10,014.80.
All Sensex components were trading in the positive territory with Tata Steel as the top gainer in the pack, jumping around 5 per cent. ICICI Bank, HDFC, Bajaj Finance, IndusInd Bank, HDFC Bank, Infosys, Kotak Bank and SBI were also among the gainers.
In the previous session, the BSE barometer settled 552.09 points, or 1.63 per cent, lower at 33,228.80, while the broader Nifty tumbled 159.20 points, or 1.60 per cent, to close at 9,813.70.
On a net basis, foreign institutional investors sold equities worth Rs 2,960.33 crore in the capital market on Monday, provisional exchange data showed.
According to traders, global markets gained after US Federal Reserve launched a massive programme to support Main Street businesses hit by the coronavirus-induced lockdown.
The Fed announced its Main Street Lending Program and an emergency lifeline under which it will buy up to USD 750 billion in corporate bonds.
The plan is part of a massive financial backstop put in place by the bank to protect the economy from the worst of the virus crisis.
Stock exchanges on Wall Street ended on a positive note in overnight trade.
Bourses in Shanghai, Hong Kong, Tokyo and Seoul rallied up to 4 per cent in early deals.
International oil benchmark Brent crude futures fell 0.53 per cent to USD 39.51 per barrel. ANS DRR DRR