The Federal Reserve is expected to announce the start of the gradual rate rise process at 19:00 GMT.
US markets opened higher, but lost ground as oil prices slumped.
A US rate rise would have global repercussions, and could adversely affect emerging economies, experts say.
The Fed is expected to raise its benchmark overnight interest rate from near zero, encouraged by a strengthening US labor market.
Analysts have been speculating for months as to when the first rise might be, with global stock markets rising and falling as Fed rate meetings come and go.
Low interest rates have generally been helpful for stock market investors, but Fed officials have indicated the likely decision in advance, removing some of the uncertainty that investors dislike.
In London, the FTSE 100 gained 0.72% by the close of the market. Paris and Frankfurt markets made smaller gains.
Many Asian markets closed significantly higher – Japan’s Nikkei 225 gained 2.6%, and Hong Kong’s Hang Seng rebounded, rising 2%.
Markets have already priced in a US rate rise, but investors will also be looking at the Fed’s announcement to gauge the likely path of future rate rises, analysts said.
The prospect of gradual rises could bring some stability to markets, but if the Fed were to raise rates more quickly, markets may take fright, analysts said.
The World Bank warned in September that a US rate rise could increase the risks to emerging economies caused by disruptions to capital flows.
With the US offering better returns, investors may decide to move money out of emerging economies.
Foreign governments could also have to pay more for debt issued in US dollars.
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