The two banks have benefited as investors bet Trump's expected fiscal stimulus will trigger inflation and stoke a rise in interest rates.
In Europe, In Europe, the FTSEurofirst 300 index of leading regional shares rose 1.3 percent and Germany's DAX rose 1.89 percent to a fresh 18-month high, while France's CAC 40 Index rose 1.17 percent.
Earlier in Japan, the Nikkei advanced 1.4 percent, buoyed by data showing the country's exports rose for the first time in 15 months in December, a positive sign for the economy even as talk of U.S. protectionism looms over the outlook.
Trump signed two executive orders on Tuesday to move forward with construction of the Keystone XL and Dakota Access oil pipelines, rolling back key Obama administration environmental actions in favor of expanding energy infrastructure.
He also met chief executives of the Big Three U.S. automakers to push for more cars to be built in the United States.
Dollar Down
Global bond yields rose as Trump shifted his focus back to growth initiatives including promising corporate tax breaks to fuel U.S. investment, after focusing on protectionism in his first few days in office.
The yield on the benchmark 10-year U.S. Treasury rose to 2.505 percent, with prices falling 8/32.
European yields rose further. Germany's 10-year Bund yield hit a six-week high of 0.389 percent and France's benchmark 10-year yield hit a one-year high of 0.95 percent . Bond prices were weighed down by the rally in stocks and new debt supply.
In currencies, the dollar failed to carry on its upward momentum from Tuesday.
Lingering concerns about growing protectionism and the potential negative effects on global trade and growth remained close to the surface. In this environment, the outlook for the Federal Reserve is murky.