About 25 minutes after the Fed's 1900 GMT announcement, the Dow Jones Industrial Average was at 17,614.16, up 89.25 points (0.51%), almost 50 points above its level prior to the announcement.
The broad-based S&P 500 rose 12.94 (0.63%) to 2,056.35, while the tech-rich Nasdaq Composite Index advanced 29.56 (0.59%) to 2,056.35.
The Fed raised the benchmark federal funds rate, locked near zero since the Great Recession, by a quarter point to 0.25-0.50%, saying the economy is growing at a moderate pace and should accelerate next year.
The move initiates what will be a series of slow rate increases which the Federal Open Market Committee, the Fed's policy board, promised would be "gradual" and follow the pace of the economy.
"What that market appreciates is the word 'gradual,'" said Gregori Volokhine, president of Meeschaert Capital Markets. "There is no surprise here."
The dollar gave back much of its bounce from the decision, with the euro trading at $1.0945, up from $1.0930 Tuesday night.