Heavy buying by foreign investors and positive global cues lifted the Sensex by 442 points to 37,496 in early trading on Tuesday while the Nifty was up 129 points at 11,297.
Metal, oil and gas, banking and energy stocks led the gains amid cheerful mood in markets that was largely driven by sustained foreign fund inflows.
Larsen & Toubro shares jumped by nearly 4 per cent to trade at Rs 1,394.55 on Bombay Stock Exchange.
ICICI Bank shares gained by more than 3 per cent to Rs 390.75 while HDFC Life Insurance shares were up by 4.5 per cent to Rs 372.60.
Jet Airways gained more than 2 per cent to Rs 253.15.
Meanwhile, Asian shares rose after the European Commission agreed to changes in the Brexit deal ahead of a vote in British Parliament.
On Monday, European Commission head Jean-Claude Juncker agreed to additional assurances in an updated Brexit deal with British Prime Minister Theresa May.