Most respondents had expected the central bank to only change the stance, to neutral from "calibrated tightening".
The repo rate is the rate at which the Reserve Bank lends short-term money to the banks, while the reverse repo rate is the rate at which the central bank borrows money from commercial banks.
In its December monetary policy review, the RBI had kept interest rates unchanged but held out a promise to cut them if the upside risks to the inflation do not materialise.
The rate cut continues a trend in which some major central banks, anxious about slowing global growth and helped by cooling inflation, have moved firmly away from last year's tightening moves or tones.
The ruling Bharatiya Janata Party is already in an election mode.
Justifying its decision to cut rates, the MPC said headline inflation is projected to remain soft in the near term "reflecting the current low level of inflation and the benign food inflation outlook". In its budget on February 1, it has doled out cash to farmers and tax cuts to middle-class families, at the cost of a wider fiscal deficit and larger borrowing.
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Monetary policies have never been about Reserve Bank of India (RBI) governors (the individual) alone ever since the formulation of Monetary Policy Committee (MPC).
Data released by the Central Statistics Office (CSO) showed consumer price index (CPI) based inflation at an 18-month low of 2.19 per cent in December against 2.33 per cent a month ago, as food prices continued to slide.
For April-September, the MPC lowered its projection on headline inflation to 3.2-3.4 percent from the 3.8-4.2 percent seen in December. This was the first MPC meeting chaired by new RBI Governor Shaktikanta Das.
The MPC voted 4:2 in favour of the rate cut, while the decision to change policy stance was unanimous.
A former economic affairs secretary, who now has the charge of central bank and is perceived to be close to the Union government, will not take "no" from banks on rate cuts too quickly.
RBI Governor Shaktikanta Das cut the interest rate by 0.25 percent to 6.25 percent, a move that will lead to reduction of lending rate by banks leading to lower EMI for housing, auto loan and corporate borrowers. The 25 bps rate cut has come after a period of one-and-a-half years (the last one was in August 2017).
The rupee weakened to 71.69 to the dollar immediately after the decision, but it later strengthened to 71.42.