The pan-European FTSEurofirst 300 index closed up 0.7 per cent after volatile trade as the banks pushed higher, but the market pared earlier gains as oil majors tracked crude prices lower.
The index rose for a third straight day to end higher at 903.61 points, but considerably off the day's high of 922.56.
London's FTSE 100 index ended up 1.2 per cent, Germany's DAX closed 1.3 per cent higher and France's CAC 40 finished having gained 0.2 per cent.
Crude dropped to around $65 a barrel as the European stock market closed, pressured by concerns that demand might continue to weaken following the shrinking of the US economy in the third quarter.
Deutsche Bank gained 14.4 per cent after the group avoided a third-quarter loss thanks to new accounting rules.
David Buik, a partner at BGC Partners, a UK broker, said: "Deutsche Bank results were much better than expected. This is influencing gains in the banking sector to a degree.
"The banking sector is also at horribly low valuations, unrealistic of their true values, and investors are now starting to put money in."
Banco Santander, UniCredit, Credit Agricole, Credit Suisse and UBS all ended up.
Gold rose to near a one-week high on safe-haven buying as the US dollar posted its biggest one-day drop in 23 years following the federal reserve's cut of half a percentage point.
Earlier, Tokyo's benchmark Nikkei 225 ended up nearly 10 per cent, or 818 points, to 9029.76.
The Nikkei has now risen 26 per cent in the past three sessions after hitting a 26-year low last week.
In Hong Kong, the Hang Seng index jumped nearly 13 per cent, while in Seoul, South Korea's Kospi index witnessed a record day, surging nearly 12 per cent.