After opening the day on a positive note at 5,982.60, the Nifty gained momentum and breached the 6,000-mark during late morning trade, the first time since January 6, 2011 when the index settled at 6,048.25.
In the afternoon trade, Nifty was trading at 6,001.90, up 0.86 per cent.
Meanwhile, the BSE benchmark Sensex was trading 145.78, or 0.74 per cent up at fresh 20-month high of 19,726.59 points, a level last seen in April 2011.
"The new year has begun on a bullish note and market can touch an all-time high before March. It is a big celebration time for markets. I think it would attract lot of people to the market who are sitting on the fence," Motilal Oswal Financial Services CMD Motilal Oswal said.
Brokers said apart from positive global cues after US fiscal cliff deal, expectations of a rate cut by the Reserve Bank of India later this month boosted the market sentiments.
"Sustained foreign funds inflows and widespread buying by retail investors, helped Nifty to breach 6,000 point level", said Deepak Pahwa, a Delhi-based stock broker, said.
ICICI Bank was trading 1.09 per cent higher, while SBI rose by 0.92 per cent.
Among others, Indusind Bank jumped 2.82 per cent, Yes Bank (1.98 per cent), Axis Bank (1.85 per cent), PNB (1.75 per cent) and HDFC Bank (0.44 per cent).
Led by gains in these stocks, the Bank Nifty index moved up by 1.06 per cent to 12,788.35.
The 30-share BSE benchmark Sensex was trading 134.84 points higher at 19,715.65 at 1355 hrs.
Overcoming Republican resistance, the US House of Representatives late yesterday night passed the "fiscal cliff" bill by 257 to 167 votes, ending a dramatic New Year's Day showdown over income taxes and deep federal spending cuts.
The bill, which was passed by the Senate (89 to 8 votes) in the wee hours of the New Year, would now go to the White House for US President Barack Obama to sign into law, which would end months of anxious moments with regard to fiscal cliff.
Had not passed, fiscal cliff would have resulted in increased tax rates for more than 98 per cent of Americans.