The Sensex gained as much as 600 points to 27,947 and the 50-share Nifty jumped over 2 per cent above the 8,450 mark. The rupee also soared by 46 paise to trade at a fresh one-month high of 61.72 against the dollar.
Rate-sensitive stocks like banks, auto, realty surged, pushing the benchmark indices higher.
State Bank of India, ICICI Bank and Punjab National Bank, were up above 3 per cent each to be among the top gainers in Nifty.
The Bank Nifty was up over 3 per cent after making a fresh 52-high of 19,410.40.
The auto index was up 1.45 per cent, while the realty index added more nearly 6 per cent. DLF was the top gainer in Nifty with 5.2 per cent gains.
As of 11.31 a.m. the Sensex was up 527 points at 27,874.49, while the Nifty traded 1.91 per cent higher at 8,435.65.
The rate cut pushed the benchmark 10-year bond yield to 7.65 per cent, down 12 basis points on the day and its lowest level since July 15, 2013.
Although markets had been widely pricing in a RBI rate cut, most investors had expected the central bank to move either at its policy review on Feb. 3 or sometime after the government unveiled its annual budget at the end of February.
Instead traders were caught off guard, as the RBI cut its repo interest rate by 25 basis points to 7.75 per cent, citing easing inflation and government efforts to contain the fiscal deficit.
"The statement was dovish in our view and with the disinflationary trend being strong, we see room for a further rally in bonds, in line with our economists forecast of more repo rate cuts," strategists at Barclays wrote in a note.
"We revise our 10 year government bond year-end target lower to 7.25 per cent from 7.40 per cent previously and continue to recommend being overweight duration in government bonds," the note added.
(With agency inputs)