The index was boosted by heavyweights Reliance Industries, TCS and HDFC Bank. Twelve of the 13 sectoral indices gained, led by metals, banks and IT stocks.
Sesa Goa, which rose 7.21 per cent, was the top gainer on the index. Bajaj Auto climbed 5.1 per cent after the company reported better-than-expected September sales.
The 30-share Sensex opened higher at 19,585.79 and advanced to the day's high of 19,929.24 before ending at 19,902.07, a gain of 384.92 points or 1.97 per cent.
"With the US government shutdown, the likelihood of the Fed tapering its quantitative easing program any time in the immediate future is reduced, thus helping the Indian equity and currency markets," said Raghu Kumar, co-founder of brokerage firm RKSV.
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A delay in tapering the Federal Reserve's monetary stimulus would ease concerns about investors pulling out from emerging market assets.
Trading sentiment also strengthened after the rupee gained against dollar.
Asian stocks ended mixed after a measure of China's service sector rose. The Hang Seng index in Hong Kong gained 1 per cent and the Taiex index in Taiwan climbed 1.73 per cent. Japan's Nikkei 225 was down 0.09 per cent while the Straits Times Index in Singapore eased 0.25 per cent.