The 30-share index gained 488.19 points, or 2.19 per cent, to trade at 19,055.74, with all sectoral indices trading in the positive zone rising up to 7.53 per cent.
Banking, realty, capital goods and consumer durables stocks were leading gainers.
The wide-based National Stock Exchange index Nifty rose by 153.80 points, or 2.82 per cent, to trade at 5,601.90.
Rajan also hinted at a shift in focus from inflation control, doggedly pursued by his predecessor, to boosting growth.
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Brokers said further recovery in the rupee also supported the upside in equities. The rupee gained 138 paise against dollar to 65.69 in early trade.
In the Asian region, Hong Kong's Hang Seng index rose by 0.95 per cent, while Japan's Nikkei was up by 0.61 per cent in early trade.