Rising for the sixth straight session, the BSE Sensex vaulted 704.37 points or 1.68 per cent to close at its lifetime peak of 42,597.43. Intra-day, it touched its all-time high level of 42,645.33.

The previous closing record for the Sensex was 41,952.63, hit on January 14, 2020.

Similarly, the broader NSE Nifty climbed 197.50 points or 1.61 per cent to finish at its all-time high of 12,461.05. It hit its record level of 12,474.05 during the day.

IndusInd Bank was the top gainer in the Sensex pack, spurting 4.95 per cent, followed by Bharti Airtel, ICICI Bank, Axis Bank, PowerGrid, Tata Steel, Titan and HDFC Bank.

Only three index constituents closed in the red -- ITC, Maruti and Bajaj Finserv, slipping up to 0.66 per cent.

World markets marched higher after Biden was declared the winner in the tightly-contested US election, though President Donald Trump has yet to concede the race.

Toning down of trade war rhetoric and a likely sharper focus on combating the COVID-19 pandemic in the US augur well for equities, analysts said.

"Firm global cues and a clear majority to favourite Democratic Party in the US election took main benchmark indices to all time high. The rally in the domestic market was also led by banking and finance stocks on improved business outlook post Q2 results, end to moratorium and bounce back of economic activities.

"Broader market has shown under-performance compared to headline peers as investors feel safer chasing heavyweights during high market levels. We expect more stimulus measures are required to boost the economy and announcements regarding the same from the government is expected in the near future that can further accelerate our domestic market," said Vinod Nair, Head of Research at Geojit Financial Services.

BSE telecom, bankex, power, metal, finance, consumer durables and teck indices rallied up to 3.81 per cent, while healthcare ended in the red.

Broader BSE mid-cap and small-cap indices rose up to 1.01 per cent.

Elsewhere in Asia, bourses in Shanghai, Hong Kong, Seoul and Tokyo ended up to 2.12 per cent higher.

Stock exchanges in Europe were also trading with robust gains in early deals.

FPIs purchased shares worth a net Rs 4,869.87 crore on Friday, according to provisional exchange data.

Meanwhile, international oil benchmark Brent crude was trading 2.26 per cent higher at USD 40.34 per barrel.

The rupee surrendered all its early gains to settle 7 paise lower at 74.15 against the US dollar, in line with weaker Asian peers against the greenback.