Hopes that the United States and China could call a trade war ceasefire at the upcoming G20 summit in Argentina also boosted stocks around the globe.
Meanwhile, the dollar retreated with potentially fewer rate increases on the horizon, and sterling rose after the Bank of England said the British economy could shrink by as much as 8 percent in about a year after a no-deal Brexit.
Equity investors reacted favourably to Powell's comments, which indicated there may not be as many rate hikes from the Fed in the future as initially anticipated.
"It’s certainly a change of language and welcome news to investors," said Jack Ablin, chief investment officer at Cresset Wealth Advisors in Chicago. "It makes the value of risk aversion less attractive so it makes risk taking, such as stock investments, more attractive."
U.S. President Donald Trump has recently been critical of the Fed for raising rates.
The Dow Jones Industrial Average rose 617.7 points, or 2.5 percent, to 25,366.43, the S&P 500 gained 61.61 points, or 2.30 percent, to 2,743.78 and the Nasdaq Composite added 208.89 points, or 2.95 percent, to 7,291.59.
The pan-European STOXX 600 index was down 0.01 percent and MSCI's gauge of stocks across the globe gained 0.08 percent.
Earlier, hopes for a U.S.-China truce on trade had also helped lift equities.
Despite Trump's tough remarks on the trade dispute ahead of Saturday's meeting with Chinese President Xi Jinping, markets focused on comments by White House economic adviser Larry Kudlow, who indicated the two countries could call a truce.
Still, lingering caution that the two sides would leave the summit without an agreement capped gains in Europe, where auto stocks were under pressure after a report Trump may soon impose new import tariffs.
A rapprochement between the United States and China is seen as crucial, given that world growth and trade are already showing signs of an alarming slowdown.
(For graphic on World Trade Organization (WTO) outlook, click https://tmsnrt.rs/2RlhEOc)
Uncertainty over global trade as well as Brexit and Italy's conflict with the European Union had supported the U.S. dollar, but the dollar index <.DXY> dipped 0.53 percent after Powell's comments. Gold prices
It said Britain risks suffering an even bigger hit to its economy than during the global financial crisis 10 years ago if it leaves the EU in a worst-case Brexit scenario.
"Our job is not to hope for the best but to prepare for the worst," BoE Governor Mark Carney said.
Some market participants took the remarks as a good sign.
"I think he's assuaging fears, saying that they’re willing to do anything they need to do,” said Michael Skordeles, U.S. macro strategist at SunTrust Advisory Services in Atlanta, regarding the bank's response to Brexit.
U.S. government bond prices were mixed following the Fed chair's speech.
Benchmark 10-year Treasury notes
The 30-year bond
U.S. crude oil futures