The 30-share BSE Sensex climbed 268.31 points to 65,923.46 in early trade. The Nifty went up by 85.1 points to 19,779.10.
Among the Sensex firms, JSW Steel, Tata Steel, Titan, Reliance Industries, HDFC Bank and Infosys were the biggest gainers.
Larsen & Toubro, Maruti, Nestle and Hindustan Unilever were among the laggards.
In Asian markets, Seoul, Tokyo, Shanghai and Hong Kong were trading with gains.
The US markets ended in the positive territory on Monday.
“The global cues are supportive. The softening US bond yields (the 10-year yield is at 4.41 per cent) will provide the big global macro backdrop for a market rally,” VK Vijayakumar, chief investment strategist at Geojit Financial Services, said.
Global oil benchmark Brent crude declined 0.44 per cent to $81.96 a barrel.
Foreign Institutional Investors (FIIs) offloaded equities worth Rs 645.72 crore on Monday, according to exchange data.
The BSE benchmark declined 139.58 points or 0.21 per cent to settle at 65,655.15 on Monday. The Nifty slipped 37.80 points or 0.19 per cent to 19,694.