The Sensex posted its biggest daily gain in more than two months as investor sentiment turned positive on growing hopes the government would push through reforms to stimulate growth and avoid a ratings downgrade.
Expectations for higher returns in December also boosted sentiment for shares.
The market also tracked global peers, which rose on new debt targets for Greece and a political agreement on disbursing the next instalment of aid. Sentiment was also helped by ratings agency Moody's maintaining India's rating outlook at stable.
The market was eagerly awaiting a media briefing by Finance Minister P. Chidambaram later in the day.
He is expected to outline the government's steps to push through with economic reforms, though opposition lawmakers are demanding the government roll back its plans to open up the supermarket sector to foreign chains.
Moody's said on Tuesday the outlook on its Baa3 rating for India is stable, citing the country's large, diverse economy and strong gross domestic product growth as supportive of the rating.
"A light market has risen on factors like Greece, increasing support on reforms and Moody's statement. The finance minister's press conference would be a further positive," said Vivek Mahajan, head of research, Aditya Birla Money.
The Sensex was up 1.65 percent, or 305.07 points, at 18,842.08, its higest close since November 8, and is just 295 points away from year high.
The Nifty gained 1.62 percent, or 91.55 points, to 5,727.45. Both the indices posted their biggest gains since September 21.
The stock market will be closed on Wednesday for a religious holiday.
Export-driven technology shares such as Infosys
The rupee could remain under pressure in the near-term due to a widening fiscal gap, with hopes diminishing for dollar inflows as the parliament remains in a deadlock over reforms, which could bring in much-needed foreign investment.
Shares in Pantaloon Retail India Ltd
Wind turbine maker Suzlon Energy Ltd