The Nifty50 on the National Stock Exchange (NSE) also rose over 100 points to trade near the 11,800 mark.
Banking, finance and auto stocks led the sector-wide gains in the Indian market. A positive trend in the Asian markets also supported the domestic indices.
Around 10.35 a.m., Sensex was at 40,158.59, higher by 401.01 points or 1.01 per cent from its previous close of 39,757.58.
It opened at 39,990.75 and has so far touched an intra-day high of 40,217.27 and a low of 39,952.79 points.
The Nifty50 on the National Stock Exchange was trading at 11,788.25, higher by 119.10 points or 1.02 per cent from the previous close.