This is the highest closing for the rupee since August 10, 2015, when it had ended at 63.87.
Frantic unwinding of long dollar positions by speculative traders ahead of key event in the US also largely supported the upmove, a forex dealer said.
The overall forex market sentiment witnessed a sustained buoyancy amid record-breaking domestic equities taking cues from global markets.
Financial markets worldwide were lifted by a strong overnight Wall Street lead.
It was a breathtaking rally for the home currency as it scaled an intra-day high of 63.93 briefly during the early morning trade.
The US president Donald Trump is expected to announce his business friendly tax policy plans later in the day.
Indian bourses continued their spectacular record setting climb for the third consecutive session with the flagship Sensex closing above the 30,000 milestone for the first time ever, while the Nifty ended at a new peak.
But later it gave back some early strong gains and finally ended at 64.11, showing a solid gain of 15 paise or 0.23 per cent.
It has appreciated by a whopping 50 paise in three day surge.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.0013 and for the euro at 70.0430.
In worldwide trade, the greenback traded higher against its major trading rivals. The dollar index, which tracks the US currency against a basket of six major rivals, was down 0.27 per cent at 99.00.
The local currency shot up against the Japanese Yen to close at 57.62 per 100 yens from 58.14 yesterday.
In the forward market today, premium for dollar displayed a steady to firm trend.
The benchmark six-month premium for September was quoted at 141-142 paise from 140-142 paise, while the far-forward March 2018 firmed up to 303-304 paise from 298-301 paise on Tuesday.
In the global commodity front, crude prices drifted on the back of a rise in US crude inventories even as record supplies around the world cast doubt over OPEC's ability to cut output and tighten the market.
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