The Sensex closed up 63.14 points, or 0.21 per cent, at 29,648.99.
The headline index of BSE, which opened at 29,755 against the previous close of 29,585, hit an intraday high and low of 29,824 and 29,601, respectively. But it ended at 9,160.05 - a new high - up 6.35 points, or 0.07 per cent, surpassing yesterday's close of 9,153.70.
The U.S. central bank on Wednesday raised interest rates by quarter of a percentage as expected, while maintaining the outlook for two more increases this year and three in 2018. Experts said this has removed concerns of foreign fund outflows from emerging markets such as India.
Some market watchers had recently speculated the Fed could hike rates four times this year as the US economy gathers momentum.
Remaining net buyers of equities in the current month so far, FIIs on Thursday purchased shares to the tune of Rs 1,360.10 crore, according to provisional data.
European stocks gained after the election victory of Dutch Prime Minister Mark Rutte who fought off a challenge from anti-immigration, anti-European Union rival Geert Wilders.
The rally in markets was mostly driven by policy stance revealed by US Federal Reserve that it will keep interest rates in the range of 0.75 per cent to 1 per cent going ahead in the new fiscal.
"The Fed makes the world safe for risk until June", said CitiFX strategist Steven Englander.
A firm trend across Asian markets is also aiding sentiment.
Among Nifty stocks, ITC was the top gainer rising 4.77 per cent followed by HCL Tech, Infosys, Wipro and Eicher Motors, which grew between 0.7-1.25 per cent.
The Fed hiked lending rates for the third time since the 2008 global financial crisis.
Buying was witnessed across the spectrum led by Realty, FMCG, Consumer Durables, Capital Goods, Power, Metal, Banks, Auto, HealthCare, IT, PSUs, Oil and Gas and Teck sectors, well supported by shares of Midcap and SmallCap companies.