The German share price index DAX graph is pictured at the stock exchange in Frankfurt, Germany, January 30, 2019.
A stronger focus on risks to the global outlook, the Fed's emphasis on tighter financial conditions and Powell's comments pushed two - and five-year Treasury yields to the lowest since mid-January.
Apple shares jumped nearly 7 percent on Wednesday after soothing China worries while Facebook shares leapt 11 percent after hours on better-than-expected profits following a year of high profile data scandals. The Nasdaq jumped 1.37 percent after a near 11 percent rise in Facebook Inc.
Pleased by the Fed's benign outlook, investors sent the Dow Jones Industrial Average up almost 435 points and back above the 25,000 level.
"It's hard to read this as anything other than the Fed has capitulated to the market", said Michael Gapen, chief United States economist at Barclays Plc.
"The market is very aggressively discounting any positive outcomes this year" in areas such as domestic growth, trade and the global economy, said Ed Al-Hussainy, a senior interest-rate strategist at Columbia Threadneedle.
The Federal Reserve signalled it's done raising interest rates for at least a while and will be flexible in reducing its bond holdings, a sweeping pivot from its bias toward tighter monetary policy just last month.
Powell, who was hand-picked by President Trump for the Fed's top spot, recently attracted scorn from the president for the Fed's rate-hiking path in 2018. "We're never going to take political considerations into account", he said. The pan-European STOXX 600 index fell 0.2 percent.
It jumped as high as 72.7 U.S. cents - but within half an hour, its gains moderated to 72.5 USA cents, at 7:15am (AEDT).
"What Apple is showing us is that when expectations have already come down and aren't getting any worse, then the markets have room to bounce", said Tom Plumb, Chief Investment Officer at Plumb Funds in Madison, Wisconsin.
Although European markets opened higher, stock fell as banks reported poor earnings.
After nine increases since the end of 2015, its target for the federal funds rate - the basis for the cost of credit card borrowing and auto loans - stood at 2.25 percent to 2.5 percent, compared with 0.5 percent three years ago. The Japanese yen firmed 0.12 percent versus the greenback at 108.92 per dollar.
The optimism supported Wall Street with the S&P 500 ending Thursday with a gain of 0.86 per cent. USA crude futures were flat at $53.79 per barrel, while Brent rose 0.2 percent to $60.93.
USA crude futures fell 0.4 per cent to $53.56 per barrel, while Brent fell 0.3 per cent to $60.65.