Stronger Chinese trade figures and the shelving of another U.S. debt limit battle also helped to shore up markets, which appear to be getting over the recent turmoil that was prompted by uncertainties over emerging economies.
Gains in Europe accelerated by midday, tracking the overnight rise recorded in Asia after Janet Yellen's remarks on Tuesday.
Though Yellen indicated that she would continue with the reduction in the Fed's stimulus, she stressed that interest rates would remain at low levels for many more months at least. That message was similarly reiterated by Bank of England Governor Mark Carney.
"It seems that investors are now convinced that the correction is over and are once again happy to buy the dips, although maybe not quite as aggressively as they were at times last year," said Craig Erlam, market analyst at Alpari.
Britain's FTSE 100 added 0.4 percent to 6,698.22 and France's CAC 40 rose 0.5 percent to 4,304.91. Germany's DAX climbed 1 percent to 9,568.42.
Futures augured a higher open on Wall Street, with Dow and S&P futures both up 0.1 percent.
The dollar has been broadly steady in the of Yellen's remarks. The euro was down 0.4 percent at $1.3579 while the dollar fell 0.2 percent to 102.26 yen.
Earlier in Asia, worries about China's economy were eased after the government reported faster growth in imports and exports for January. That helped stocks across the region to post solid gains, including China's Shanghai Composite Index, which ended 0.3 percent higher.
Elsewhere, Japan's Nikkei 225 gained 0.6 percent to finish at 14,800.06. Japanese markets were closed Tuesday for a national holiday. Hong Kong's Hang Seng surged 1.5 percent to 22,285.79 and South Korea's Kospi added 0.2 percent to 1,935.84.
AP Business Writer Yuri Kageyama in Tokyo contributed to this report.