However, dollar buying by state-run banks and a rise in oil prices capped the rupee gains, forex traders said.
At the interbank foreign exchange market, the rupee opened strong at 83.30 against the last close of 83.40, the lowest closing level against the US dollar.
The rupee moved in a tight range of 83.35 and 83.27 in the day trade. It finally closed at 83.30, up by 10 paise over the previous close.
The US dollar index, which measures the greenback's strength against a basket of six currencies, eased by 0.32 per cent to 102.54.
The US Federal Reserve kept its key interest rate unchanged on Wednesday for a third time in a row. The officials also signalled that they expect to make three quarter-point cuts to their benchmark rate next year.
"The crash in the US 10-year yield to 4 per cent will trigger large capital flows to India. The main beneficiaries will be the large caps, particularly the fairly valued large caps in banking. IT too is likely to attract buying," VK Vijayakumar, Chief Investment Strategist at Geojit Financial Services said.
Brent crude futures, the global oil benchmark, rose 2.11 per cent to USD 75.83 per barrel.
In the domestic equity market, the 30-share BSE Sensex jumped 929.60 points to settle at an all-time high of 70,514.20. The 50-issue Nifty climbed 256.35 points to settle at a record of 21,182.70.
Foreign Institutional Investors (FIIs) were net buyers in the capital market on Thursday as they bought shares worth Rs 3,570.07 crore, according to exchange data.