After touching a peak of 36,806.30 during the day, the 30-share BSE Sensex settled 408.68 points, or 1.12 per cent, higher at 36,737.69.
Similarly, the NSE Nifty jumped 107.70 points, or 1.01 per cent, to finish at 10,813.45.
Both the indices closed at four-month highs.
Bajaj Finance was the top gainer in the Sensex pack, spurting 3.93 per cent, followed by SBI, Tata Steel, HDFC, Bajaj Finserv, HCL Tech and Axis Bank.
In value terms, HDFC, Reliance Industries and HDFC Bank contributed to most of the gains on the Sensex.
On the other hand, ONGC, Tech Mahindra, Maruti, TCS, HUL and ITC were among the laggards, skidding up to 1.66 per cent.
Meanwhile, wooing global companies, Prime Minister Narendra Modi on Thursday said Asia's third-largest economy is one of the most open in the world and offers investment friendly, competitive business environment and immense opportunities.
Speaking at the India Global Week 2020, he said green shoots of economic revival are already visible in India that is coming out of coronavirus lockdown.
Vinod Nair, Head of Research at Geojit Financial Services at Geojit Financial Services, said, "In spite of rising concerns regarding the spread of the virus infections, markets continued to focus on the path to recovery in the economy. With liquidity giving adequate support, investors are looking towards the start of the earnings season."
"With the lockdown and the economic activity coming to a standstill in the last quarter, investors will be looking forward to the earnings commentary, to understand the outlook," he added.
BSE metal, finance, bankex, basic materials, energy and telecom indices surged up to 2.13 per cent, while FMCG, power and capital goods ended with losses.
Broader BSE mid-cap and small-cap indices rose up to 0.49 per cent.
On the global front, Chinese equities led other Asian markets higher. Bourses in Shanghai, Hong Kong, Tokyo and Seoul ended with significant gains.
Stock exchanges in Europe too opened on a positive note.
International oil benchmark Brent crude futures inched up 0.05 per cent to USD 43.31 per barrel.
In the forex market, the rupee settled 3 paise higher at 74.99 against the US dollar.
India saw a record single-day surge of 24,879 COVID-19 cases taking the caseload to 7,67,296 on Thursday, while the death toll climbed to 21,129, according to the Union Health Ministry data. ANS ANS ABM ABM