The 30-share barometer rose by 121.82 points, or 0.63 per cent, to 19,486.57 with all sectoral indices led by auto and metal stocks leading the rise.
The wide-based National Stock Exchange index Nifty traded above crucial 5,900 level higher by gaining 34.15 points, or 0.58 per cent, to 5,930.95.
Brokers said the sentiment remained firm on sustained buying by funds and retail investors on optimism of RBI easing monetary policy next month.
They said a firming trend in the Asian region, tracking overnight Wall Street's gains where optimism was growing that a deal to avert the fiscal cliff was in sight also influenced the sentiment.
In the Asian region, Hong Kong's Hang Seng rose by 0.71 per cent, while the Japan's Nikkei by 1.01 per cent in early trade today. The US Dow Jones Industrial Average ended 0.87per cent higher yesterday.