In opening trade, London's FTSE 100 index of top companies jumped 1.28 percent at 5,973.07 points, Frankfurt's DAX 30 index won 1.01 percent to 7,689.46 points and in Paris the CAC 40 rallied 1.73 percent to 3,703.97.

"It may have come at the last minute, but US lawmakers finally managed to find some common ground by voting through a package of policies designed to avoid the immediate fiscal cliff," said ETX Capital trader Joe Rundle.

"Financial markets have responded accordingly with Asian shares performing strongly and European markets posting sharp gains in the first trading day of 2013 and US markets are likely to react in the same fashion."