The NSE Nifty 50 index ended 1.87% higher at 11,095.25, while the S&P BSE Sensex closed up 2.03% at 37,687.91.

Shares of private sector lender HDFC Bank closed nearly 4% higher after the Reserve Bank of India (RBI) approved Sashidhar Jagdishan's appointment as the new chief of the country's most valuable bank.

Data showing U.S. manufacturing activity accelerated to its highest level in nearly one and a half years in July, further boosted sentiment and lifted Asian shares. MSCI's broadest index of Asia-Pacific shares outside Japan advanced 0.9%.

"Global cues are positive and RBI approval for the CEO seat at HDFC Bank is supporting domestic markets," said Rahul Sharma, head of research, Equity99 Advisors in Mumbai.

In Mumbai trading, shares of India's most valuable company Reliance Industries were the biggest boost, finishing 7.4% higher.

The Nifty financials index closed up 2.28% and the Nifty private banks index settled 2.02% higher.

India's small-cap and mid-cap shares rose over 1% each.

Domestic investors also await a policy rate decision due on Thursday.

Meanwhile, India reported a jump of 52,050 coronavirus infections in the last 24 hours, with the total number of cases now at 1.86 million and the death toll at 38,939, health ministry data showed.

Among losers, the Nifty IT index fell 0.88% after reports said U.S. President Donald Trump on Monday signed an executive order preventing federal agencies from contracting or subcontracting foreign workers, mainly those on H-1B visa.

By Chandini Monnappa