The 30-share index rose by 125.27 points, or 0.50 per cent, to 25,371.521 points with capital goods, power, consumer durables, realty and auto sector stocks leading the recovery.
The index had tanked 274.94 points in yesterday's trade after unrest intensified in Iraq, threatening rise in crude import costs.
On the similar lines, the National Stock Exchange index Nifty surged by 37.95 points, or 0.50 per cent, to 7,596.15.
The Fed said the economic growth has rebounded in recent months and kept its short-term interest rates unchanged.
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However, it cut its monthly bond-purchase programme to USD 35 billion from USD 45 billion.
Among other Asian markets, Hong Kong's Hang Seng rose by 0.36 per cent, while Japan's Nikkei was up by 1.62 per cent in early trade today.
The US Dow Jones Industrial Average gained 0.58 per cent higher in the previous session.