UK shares jumped 1.5% while other European indexes were also higher.
Failure to agree a deal would have triggered spending cuts and tax increases worth $600 billion.
There had been fears that the measures would have derailed the modest recovery in the world’s biggest economy and perhaps even push it back into recession.
German stocks gained by 1.6%, while France’s Cac 40 rose 1.4% and Italy’s stocks gained 2%.
In the US, the lower chamber of Congress passed a deal backing a compromise that had already passed in the Senate, which raises taxes for the wealthy and delays spending cuts for two months.
The fiscal cliff measures – cutting spending and increasing taxes dramatically – came into effect automatically at midnight on Monday when George W. Bush-era tax cuts expired.
The 31st of December deadline triggered tax increases of about $536 billion and spending cuts of $109bn from domestic and military programmes – which has now been averted.
Shares worldwide had been hurt in November and December by fears that the US would not be able to reach any kind of agreement and would go off the cliff.
Earlier, Asian shares gained on the news of the deal. The US is also a key market for most of Asia’s export-dependent economies.
The US dollar rose, jumping against the Japanese yen. The Japanese currency was at 87.30 yen against the US dollar at one point, its lowest level since July 2010.
The yen has fallen almost 9% against the US dollar since November 15.
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