The 30-share Sensex ended up 187 points or 1.03% at 18,414 and the Nifty gained 64 points or 1.16% to close at 5,559.
World shares edged up to their highest level in a week on Wednesday after Chinese trade data pointed to a steady recovery of the world's second largest economy.
China reported a mild trade deficit of $884 million in March as a 14.1% year-on-year surge in imports eclipsed export growth of 10%, signaling that domestic demand was gathering the pace needed to drive economic recovery.
MSCI's all-world share index, which tracks stocks in 45 countries, rose 0.4% to its highest level since April 3 as European shares followed gains in Asian markets.
London FTSE 100, Paris's CAC-40 and Frankfurt's DAX were up between 0.7 and 1.2% higher.
In Asia, Asian shares edged higher as Chinese trade data signaled a recovery in the world's second largest economy, adding to an improving sentiment after Wall Street closed at a record high overnight, while the yen remained under pressure.
The MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.2%, pulled higher by its materials sector with a 1.3% jump, as iron ore prices recovered.
Japan's Nikkei average climbed to its highest closing level in nearly five years, with traders citing new money coming into the market after the central bank started its ultra-loose
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