Sensex rose 1,303 points to 28,894 against the previous close of 27,590. Nifty too gained 354 points to 8,438 in early trade.
All 30 Sensex stocks except Bajaj Finance were trading in the green.
Share Market LIVE: Sensex climbs 1,300 points, Nifty at 8,400; JSW Steel climbs 5%
IndusInd Bank (17%), Axis Bank (9%) and M&M (12%) were the top Sensex gainers. On Nifty, the same set of stocks were the top gainers rising up to 18%.
Of 50 Sensex stocks, 48 were trading in the green. Bajaj Finance (2.87%) and Bajaj FinServ (1.59%) were the only losers on index.
Asian markets were trading with big gains as the number of new coronavirus cases is dropping in the European hotspots of Italy and Spain. New York also reported its number of daily deaths which has been effectively flat for two days.
Japan's Nikkei 225 gained 1.3% to 18,808.53 while South Korea's Kospi gained 1.2% to 1,812.87. Hong Kong's Hang Seng added 0.7% to 23,907.52, while the Shanghai Composite jumped 1.7% to 2,814.09.
Overnight, the S&P 500 climbed 175.03, or 7%, to 2,663.68, and nearly all the stocks in the index were higher. It more than recovered all its losses from the prior week, when the government reported a record number of layoffs sweeping the economy.
The Dow Jones Industrial Average shot up 1,627.46 points, or 7.7%, to 22,679.99, and the Nasdaq rose 540.15, or 7.3%, to 7,913.24.
By Aseem Thapliyal