The 30-share index moved higher by 149.01 points, or 0.47 per cent, to 31,440.86. The gauge had gained 33 points in yesterday's session.
All the sectoral indices led by realty, healthcare, PSU, bank and capital goods leading the gains, rising by up to 1.50 per cent.
The National Stock Exchange index Nifty too rallied by 51.15 points, or 0.52 per cent, to trade at 9,816.70.
Brokers said sentiment bolstered largely in tune with a firming trend across Asian market following overnight gains at Wall Street, driven by growing optimism over a US tax reform plan and as investors look ahead to a key central bankers meeting.
Globally, Japan's Nikkei moved up 0.46 per cent, while Shanghai Composite Index added 0.02 per cent. Korea too ticked up 0.05 per cent, Singapore rose 0.20 per cent and Taiwan gained 0.28 per cent in morning trading.
The US Dow Jones Industrial Average ended 0.90 per cent higher in yesterday.