Anticipation over the Fed's action hung over international markets ahead of the announcement, with European equity markets "treading cautiously," said a note from Schwab. London, Paris and Frankfurt all fell, along with Tokyo.
In the US, the Dow pushed to a fourth straight closing record, up 0.3 per cent at 24,585.43.
Citing the strong labour market and solid economy, the Fed's policy-setting Federal Open Market Committee, as expected, increased the key lending rate to 1.25-1.5 per cent, an increase of a quarter point.
While stock values "are on the high end of historical ranges," that could be justified in a long period of low interest rates, Yellen said.
"There's less to lose sleep about now," Yellen said, adding, "We have a much more resilient, stronger banking system. And we are not seeing some worrisome build-up in leverage or credit growth at successive levels."
Analysts said US equities also were boosted by reports that Senate and House Republican leaders reached an agreement in principal on the massive tax bill, setting the stage for final passage next week.
But the dollar pulled back as the US central bank again noted the meagre level of inflation, which has been seen as a potential hindrance to a more aggressive pace of interest rate increases.
"The Fed offered little fuel to excite dollar bulls who have gone into seclusion this year, with the broadly weighted dollar index down 8 per cent year-to-date," said Joseph Manimbo, senior market analyst at Western Union Business Solutions.
Monetary policy will be back in focus today with a meeting of the European Central Bank. The ECB is expected to highlight economic strength in the eurozone in new forecasts today, while avoiding spooking markets with talk of further cuts to its massive support for the economy.
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