The main share indexes in France, the UK and Germany’s were all up by between 1% and 3% in morning trade.
The US central bank increased the range for its benchmark interest rate to between 0.25% and 0.5%, from the previous range of 0%-0.25%.
The Fed said the rise was part of a “gradual” process to get rates back to normal after years of being near zero.
“Considerable improvement” in the jobs market spurred the Fed into action.
London’s FTSE 100 rose 1.4% to 6,146.68, while Frankfurt’s Dax jumped more than 3% and the Cac 40 in Paris was 2.5% higher.
The European stock markets were following the lead given by markets in the US and Asia.
On Wall Street, the Dow Jones closed up 224.18 points, or 1.3%, at 17,749.09, while in Japan, the benchmark Nikkei 225 closed up 1.6% at 19,353.56.
After the Fed’s decision, the dollar rose against larger major currencies. Higher rates make the US a more attractive market for deposits, meaning demand for the dollar is likely to rise.
However, sterling recovered ground lost against the dollar and was 0.3% higher against the euro to €1.3783 after positive retail sales numbers for November.
At one point £1 bought almost $1.50.
British government-issued bonds, or gilts, rose in price following the Fed decision, meaning lower yields, or income.
Benchmark ten-year gilt yields fell 0.056 percentage points to 1.89%. While the specter of higher rates is often bad for existing debt prices, analysts said investors were pleased future Fed rate rises would be “gradual” in nature.
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