The Sensex closed the day at 24,479.84, a gain of 291.47 points, or 1.21%. The Nifty ended the day with a gain of 84.10 points, or 1.14%, at 7,435.10.
The BSE has sought a clarification from Tata Motors in response to a report in The Economic Times that the company may secure an additional order for supplying high mobility trucks to the Indian Army valued at about Rs 350 crore.
The value of of the earlier order for 1,239 vehicles was Rs 940 crore, according to The Economic Times.
Shares of Tata Motors closed at Rs 354.05, up 3.71%.
Indian stock markets rallied on Tuesday, shrugging off China's 25-year-low GDP growth rate in 2015. On Monday, the benchmark indices had shed more than 1% on renewed concerns of a prolonged slowdown in the world's largest economy and depressing macroeconomic data and weak corporate earnings.
The S&P BSE Sensex was trading at 24,439, a gain of 251 points, or 1.04%, while the Nifty was up 0.93% at 7,419.60.
Bank stocks, which were battered over the past few sessions, with many of them hitting new 52-week lows, gained on value buying by investors.
Axis Bank, ICICI Bank and State Bank of India (SBI) were the biggest Sensex gainers, along with Tata Motors, Reliance Industries and Infosys.
Among bank stocks, Axis Bank was the biggest gainer at 5.23%, followed by ICICI Bank at 3.19% and State Bank of India, which was up 2.79%.
Reliance Industries, which declares its Q3 results on Tuesday, edged higher by 2.65% at Rs 1,045.
On the NSE, Axis Bank, Yes Bank, Tata Power, ICICI Bank were leading the Nifty rally.
The BSE midcap and small-cap indices were up 1.36% and 1.47%, respectively.
Other major gainers on the BSE included SpiceJet (8.74%), Srei Infra Finance (9.74%) and Pipavav Defence (6.84%).
Most of the IT stocks, including Wipro, Mindtree and HCL Technologies were in the red.
On Tuesday, China reported its economy grew 6.9% in 2015, with the last-quarter growth coming at 6.8%.
The world's second-largest economy hit a 25-year low with its 2015 GDP growth rate.
The country is likely to grow in the range of 6.4-6.5% in 2016, according to Ben Cavender, principal, China Market Research Group, a Shanghai-based market intelligence company, reported moneycontrol.com.
There are renewed concerns about the rupee, with an analyst predicting it to plunge to 69 against the US dollar due to sustained outflows from foreign institutional investors and weak corporate earnings for the third quarter.
The rupee's all-time low is 68.85, recorded on 28 August, 2013.