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London's FTSE 100 index of leading companies gained 0.35 percent to 6,450.27 points in afternoon trade, while Frankfurt's DAX 30 climbed 0.17 percent to 7,932.89 points and in Paris the CAC 40 advanced 0.42 percent to 3,789.51 points.
The euro increased to $1.3097 from $1.2971 late on Wednesday in New York, while the British pound fell against the European single currency and dollar.
Gold prices rose to $1,580.50 an ounce on the London Bullion Market from $1,574 on Wednesday.
ECB chief Mario Draghi said he believes that with the current rate, an unprecedented amount of liquidity pumped into banks and a key bond-purchase programme in place, the central bank has already done its utmost to help resolve the long-running crisis.
Following the decision, Draghi played down the impact of the Italian election result last week, noting that uncertainty had not spread to other countries or the markets.
The ECB also trimmed its growth forecasts for this year and next as the impact of the bloc's debt crisis continued to be felt in the 17-country eurozone.
The ECB said it saw the eurozone economy contracting by 0.5 percent in 2013 before recovering to grow by 1.0 percent next year. It had previously forecast -0.3 percent and 1.2 percent respectively.
The Bank of England meanwhile voted to hold its reference interest rate at a record-low 0.50 percent, where it has stood for four years, and opted against increasing its cash stimulus programme to boost a British economy on the brink of recession.
In company news, shares in Aggreko, a temporary power supplier, surged 14.28 percent to 2,009 pence after it announced a rise in annual pre-tax profits thanks to income earned on the back of last year's London Olympics.
Carrefour climbed 3.95 percent to 22.23 euros after the French supermarket giant said its 2012 net profit was three times bigger than the previous year owing mainly to asset sales.
On the downside in London, Aviva shares slumped 11.53 percent to 318.32 pence, as the British insurer slashed its shareholder dividend after revealing that it tumbled into a net loss last year.
The stock had earlier dived as low as 295 pence.
Aviva suffered a loss after taxes of £3.0 billion ($4.5 billion, 3.5 billion euros) in 2012, mainly owing to a massive writedown following the sale of its US business. That contrasted with a net profit of £60 million in 2011.
US stocks also opened higher Thursday with the Dow Jones Industrial Average up 36.11 points (0.25 percent) to 14,332.35, after setting a fresh all-time closing high Wednesday at 14,296.24.
The broad-based S&P 500 gained 3.42 (0.22 percent) at 1,544.88, while the tech-rich Nasdaq Composite rose 4.40 (0.14 percent) to 3,226.77.