The 30-share BSE index was trading 331.04 points or 0.80 per cent higher at 41,547.18, and the broader NSE advanced 93.50 points, or 0.77 per cent, to 12,201.40.
In the previous session, Sensex settled 236.52 points, or 0.58 per cent, higher at 41,216.14 and Nifty rose 76.40 points, or 0.64 per cent, to 12,107.90.
Meanwhile, on a net basis, foreign institutional investors sold equities worth Rs 209.39 crore, while domestic institutional investors bought shares worth Rs 344.63 crore on Tuesday, data available with stock exchanges showed.
HUL was the top gainer in the Sensex pack, rising up to 3 per cent, followed by Tata Steel, NTPC, HDFC, Nestle India, PowerGrid and Axis Bank.
On the other hand, IndusInd Bank was the sole laggard in morning session.
According to analysts, domestic investors are likely to stay focused on the last batch of Q3 numbers, factory output and CPI inflation for the month of January. As per the consensus, inflation is expected to remain elevated confirming the recent action by the central bank.
Market also took positive cues from global markets that remained on firm footing despite concerns over coronavirus (COVID-19), traders said.
Bourses in Shanghai, Hong Kong, Tokyo and Seoul were trading on a positive note.
Stock exchanges on Wall Street closed with gains on Tuesday.
Meanwhile, the rupee appreciated 5 paise against the US dollar to 71.21 in morning session.
Global crude benchmark Brent rallied 1.72 per cent to USD 54.94 per barrel. ANSANS