The party's success has raised hopes among investors that it could come to power with decisive strength in India's general election May and introduce pro-market reforms that could boost ailing economic growth.
The benchmark 30-share Sensex index jumped 2.32 percent to 21,483.74 in early trade, beating their previous all-time high of 21,321.
53 seen on November 3.
The rupee also strengthened against the dollar to 60.
84, its strongest level since August.
It had closed on Friday at 61.42. Benchmark 10-year bond yields eased four basis points to 8.81 percent.
"The markets have risen on the hope that the BJP can come in with decisiveness in the general elections in May," said Sonam Udasi, head of research with IDBI Capital.
"This would make decision-making and reforms easier, as it may not need to rely on alliance partners to form the government," he told AFP.
In November, investment bank Goldman Sachs hiked its rating for India's markets to "market weight" from "underweight" on optimi