On a weekly basis, the Sensex recovered 435.03 points, or 1.78 per cent, and the NSE Nifty rose 141.10 points, or 1.90 per cent, snapping three straight weekly losses.
Covering up of positions by speculators, fearing a further run-up in coming sessions, also helped the key indices rise.
A firming trend at other Asian markets, led by Japan, after the Bank of Japan surprised markets by announcing a negative interest rate policy, buoyed sentiment here too, brokers said.
Appreciating rupee against the dollar also boosted sentiment, they said.
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The 30-stock index, after opening in negative zone at 24,347.31, quickly staged a comeback and rallied to hit the session's high of 24,911.90 on across-the-board buying, tracking positive Asian cues and building-up of bets following the beginning of the February derivatives series.
Finally, the gauge settled 401.12 points, or 1.64 per cent higher, at 24,870.69.
The gauge had shed 22.82 points in the choppy session yesterday.
Top gainers among Sensex constituents included Coal India, up 4.73 per cent, followed by Hero MotoCorp, Sun Pharma, Hindustan Unilever, Dr Reddy's and Bajaj Auto.
Of the 30-share Sensex group, 25 ended higher, while 5 led by SBI, Tata Steel, NTPC, ICICI Bank and Bharti Airtel, closed in the negative territory.
Among BSE sectoral indices, Consumer durable gained the most by rising 3.26 per cent, followed by healthcare (2.51 per cent), IT (2.43 per cent), TECK (2.04 per cent), capital goods (1.93 per cent), Auto(1.91 per cent) and metal (1.78 per cent).
Meanwhile, foreign portfolio investors sold shares worth Rs 961.82 crore yesterday, as per provisional data.