Though they had faltered on Tuesday, major US indices climbed about one percent or more after Hong Kong Chief Executive Carrie Lam formally withdrew a bill that aimed to allow extradition of criminal suspects to mainland China.
Her action was in response to mass protests that had spurred fears of a crackdown by Beijing.
Meanwhile, British MPs inflicted a fresh defeat on Prime Minister Boris Johnson's hardline Brexit strategy, approving a law that could stop him from taking Britain out of the European Union next month without a deal.
The Dow Jones Industrial Average finished 0.9 percent higher at 26,335.47.
The broad-based S&P 500 gained 1.1 percent to 2,937.78, while the tech-rich Nasdaq Composite Index advanced 1.3 percent to 7,976.88.
Gregori Volokhine, fund manager at Meeschaert Financial Services, said Lam's decision in Hong Kong "removed a big worry" for investors who had feared a muscular response from Beijing to the demonstrations.
Markets have factored in the grinding US-China trade war but "a big degradation of the situation in Hong Kong has not been figured in," Volokhine added.
A report Wednesday from the Federal Reserve characterized growth as modest.
"Although concerns regarding tariffs and trade policy uncertainty continued, the majority of businesses remained optimistic about the near-term outlook," the central bank said in nationwide survey of economic activity.
Among individual companies, JetBlue Airways slid 4.5 percent as it lowered a key revenue forecast, due to weaker-than-expected demand and the expected hit to flights from Hurricane Dorian.