The 30-share index rose by 132.22 points, or 0.68 per cent, to trade higher at 19,558.93 points with all the sectoral indices led by realty and metal, trading in positive zone with gains up to 1.23 per cent.
The Sensex had shed 18.13 points in the previous session in two-way movements.
The broad-based National Stock Exchange index Nifty rose by 37.90 points, or 0.64 per cent, to 5,943.00.
Brokers said sentiments buoyed largely in tandem with overnight gains on the US markets on fresh hopes for a last-minute deal to avoid the economy-crunching fiscal cliff.
Besides, expectations of rate cut by the RBI later this month also triggered buying by participants, they said.
The US Dow Jones Industrial Average ended 1.28 per cent higher in yesterday's trade, while most of Asian markets are closed today for a public holiday.
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