Weakness of dollar in the overseas market also boosted the rupee value, a forex dealer said.
Besides, stock markets in India shot up to record levels, crossing 25,000 points - up more than 1,100 points - for the first time as election result trends poured in, indicating strong overseas inflows.
Banks and exporters preferred to reduce their dollar position on expectation of more funds on the back of strong equity market.
The rupee resumed higher at 59.00 per dollar as against the last closing level of 59.29 at the Interbank Foreign Exchange (Forex) Market.
It firmed up further to an 11-month high of 58.71 per dollar before quoting 58.73 per dollar at 1000 hours.
The domestic currency moved in a range of 59.00 and 58.71 per dollar during the morning deals.
In New York market, the dollar reversed course yesterday, falling against the Japanese yen as US Treasury yields slumped.
Meanwhile, the Indian benchmark 30-share index Sensex crossed its 25K level in the morning and was quoted higher by 1,126.64 points or 4.71 per cent to 25,032.24 at 1010 hours.