The FTSE 100 index rose 77 points, or 1.1%, to 6,911.4, with similar rises seen elsewhere in Europe.
Most analysts had expected the Fed to hold rates on Wednesday, although the US central bank indicated rates could rise before the end of the year.
The dollar fell after US rates were held, which pushed commodity prices up.
That led to rises in shares of mining companies, as the price of copper hit a one-month high and other metal prices increased.
Shares in Glencore and Fresnillo led the FTSE 100 higher, with both seeing rises of more than 5%.
"Given the rise across the spectrum for commodities, it comes as no surprise that the FTSE leaderboard is headed by some of the biggest names in mining," said Joshua Mahony, market analyst at IG.
In the FTSE 250, shares in Kier Group rose 1.3% after the construction group reported a 45% increase in underlying full-year pre-tax profits to Â£125m.
On the currency markets, the pound rose 0.55% against the dollar to $1.3104, but was little changed against the euro at â‚¬1.166.
(Close): UK shares joined in the global rally triggered by the US Federal Reserve's decision to keep interest rates unchanged.