The Bombay Stock Exchange's Sensex index jumped more than two percent to pass the 40,000 mark for the first time ever while the Nifty crossed 12,000 points, also a new landmark.
India's rupee also strengthened, hitting 69.51 against the dollar from 69.67 late Wednesday, as traders welcomed trends that showed Modi's Hindu nationalist Bharatiya Janata Party (BJP) was set to win a majority.
After almost three hours of counting, figures from the Election Commission showed the BJP in the lead in 291 seats out of 542 with the rival Congress on just 51.
If confirmed -- no results have been published yet -- this would push the BJP over the 272 seats needed for a majority.
It could also beat its tally of 282 when Modi swept to power in the world's biggest democracy in 2014 with the first majority in 30 years.
The result would give the BJP and its allies, which early trends suggested would win close to 50 seats, a commanding majority of around 330 seats.
Indian stock markets have rallied since exit polls on Sunday pointed to a Modi triumph.
On Thursday, the benchmark Sensex rose more than two percent to peak at 40,124.50, while the Nifty, a smaller index based on 50 Indian companies also increased more than two percent, touching a new record of 12,041.00.