The pan-European STOXX 600 index rose 1.7% after last week's 3.6% drop, with the banks index jumping 4.1%.
Asian markets mostly fell Monday with sentiment depressed by a spike in coronavirus infections that has forced fresh lockdowns and sparked worries about the impact on the world economy.
The pan-European STOXX 600 index were up 0.1% at 0714 GMT, with technology, automakers and oil & gas firms leading the gains.
The Nikkei 225, which snapped a six-day losing streak on Monday, added 378.28 points to close at 22,573.66, while the broader Topix index rallied 2.14 per cent, or 32.62 points, to 1,555.26.
The benchmark Nikkei 225 index slipped 0.26 per cent, or 58.81 points, to end at 22,514.85, while the broader Topix index inched down 0.04 per cent, or 0.55 points, to 1,554.71.
London's benchmark FTSE 100 index was up 1.0 per cent, in the eurozone, Frankfurt won 0.9 per cent and Paris climbed 0.8 per cent.
World stock markets took a hope on Tuesday after a second major coronavirus vaccine boost in the space of a week had propelled them higher again and put Europe on course for its best month nearly three decades.
Global stock markets jumped on Wednesday after the release of more upbeat data about the COVID-19 vaccine being developed by Pfizer and BioNTech. Traders have this month been encouraged by announcements of progress toward possible vaccines and on Wednesday
London's benchmark FTSE 100 advanced 1.1 per cent to 5,715.53 points, Paris CAC 40 rose 0.9 per cent to 4,734.09 and Frankfurt's DAX 30 was up 0.6 per cent at 11,860.97. The Shanghai Composite Index advanced 1.1% to 3,259.48 and the Hang Seng in Hong Kong rose 2.2% to 24,988.27
Tokyo is leading the Asian market with gains jumping 1.7 per cent while Sydney piled on 0.9 per cent. Euro Stoxx 50 futures fell 0.9% at 06:56 GMT, while German DAX futures shed 0.7% and UK's FTSE futures lost 0.5%.