After hitting a high of 31,400.36, the 30-share index was trading 639.83 points or 2.08 per cent higher at 31,329.85.
Similarly, the NSE Nifty was quoting 187.20 points, or 2.08 per cent, up at 9,181.05.
Sun Pharma was the top gainer in the Sensex pack, rallying up to 5 per cent, followed by L&T, HUL, Axis Bank, UltraTech Cement, ICICI Bank.
Reliance Industries jumped nearly 3 per cent after the company said it will raise Rs 9,000 crore through an NCD sale this week to refinance the existing high-cost rupee debt.
On the other hand, ONGC, Maruti, Kotak Bank and Titan were the laggards.
In the previous session on Monday, the BSE barometer ended 469.60 points or 1.51 per cent lower at 30,690.02, while the Nifty dropped 118.05 points or 1.30 per cent to 8,993.85.
Market remained closed on Tuesday for Ambedkar Jayanti.
Foreign portfolio investors (FPIs) were net buyers in the capital market in the last trading session, as they bought equity shares worth Rs 1,243.74 crore, according to provisional exchange data.
The government, after market hours on Monday, notified Mauritius as an "eligible country", enabling its investment entities to register as Category-I FPIs with lower KYC requirements.
Experts said that considering the size of investment in Indian capital market by overseas entities from Mauritius, this is a welcome move.
According to traders, positive cues on the FPI front and stock-specific action pulled the market higher. However, concerns over the spike in Covid-19 cases and an extension in the nationwide lockdown in the country kept investors cautious.
The death toll due to Covid-19 rose to 377 while the number of cases in the country climbed to 11,439 on Wednesday, according to the Union Health Ministry.
Global tally of the infections has crossed 19 lakh, with over 1.2 lakh deaths.
Meanwhile, bourses in Shanghai, Hong Kong and Tokyo were in the red.
Stock exchanges on Wall Street ended significantly higher in overnight trade.
Brent crude futures, the global oil benchmark, rose 1.35 per cent to USD 30 per barrel. ANSANS