Exit polls had predicted a clear win for Modi in the election held over April and May, and the initial counting leads came in line with those predictions.
The rupee has risen in all four sessions since the exit poll results were released on Sunday.
"The initial leads are suggesting that the BJP is going to get a majority of its own and that is very positive for all asset classes because such a mandate brings political stability.
There will be extensive capital inflows to India," said Anindya Banerjee, analyst at Kotak Securities.
Banerjee added that the extent of appreciation in the rupee might be limited now but it stood to outperform its emerging market peers in the near term.
Most other Asian currencies drifted lower but fared better than regional equities markets as stability in the Chinese yuan helped stave off pressure from U.S.-China trade tensions.
The yuan, the Singapore dollar, the Thai baht, the Philippine peso and the Malaysian ringgit weakened, but traded in narrow ranges.
"One key reason for wider Asian currency stability is the yuan staying below the 7.00 mark against the dollar. That is helping to curb the sentiment in the wider Asian currency space given that the yuan is such a big driver in the region," said Chang Wei Liang, forex strategist at Mizuho Bank.
The South Korean won firmed as much as 0.4% to a one-week peak and is set for a fourth straight session of gains.
After three consecutive months of losses and being down about 2% so far in May, the won's fortunes turned around this week.
South Korean finance ministry and central bank officials on Wednesday issued verbal warnings against disorderly currency market movements, saying the exchange rate appeared to have been "overshooting" as the won was weakening "relatively fast".
RUPIAH RECOVERS
The Indonesian rupiah bounced back from the previous session's losses as calm returned to the streets of Jakarta after clashes between security forces and protesters angry over Indonesian President Joko Widodo winning a second term.
The rupiah put on as much as 0.3% to 14,480 against the dollar, its best intraday percentage gain in three weeks. Commenting on the rupiah's recovery, analysts at Oanda said in a note that the political worries caused by overblown coverage of the riots would probably fade quickly.