The UK's FTSE 100 Index climbed 1.8 percent, France's CAC 40 Index jumped 2.2 percent and Germany's DAX Index soared 2.7 percent.
"Whether it's in the US, Japan or Europe, the market likes quantitative easing," Joe Saluzzi, co-manager of trading at Themis Trading in Chatham, New Jersey, told Reuters. "But China concerns have not gone away. I'm expecting choppiness for a while longer."
The euro dropped against the US dollar, last trading 1 percent weaker at US$1.1109.
Wall Street ended mixed, giving up earlier gains late in the day as investors repositioned for the last key data point ahead of the Federal Reserve's next policy meeting.
At about 4pm in New York, the Dow Jones Industrial Average rose 0.2 percent. The Standard & Poor's 500 Index fell 0.2 percent, and the Nasdaq Composite Index shed 0.5 percent.
Gains in shares of Intel and those of Cisco, last up 1.4 percent and 1 percent respectively, led the Dow higher, outweighing slides in shares of Caterpillar and those of Apple, last 2.7 percent and 1.9 percent weaker respectively.
All eyes are on the government's jobs reports, scheduled for release on Friday, as investors are trying to assess the odds the Fed will hike interest rates for the first time since 2006 at its next two-day meeting, starting September 16.
"There's going to be caution not only going into the jobs report but into the long weekend," Tim Ghriskey, managing director and chief investment officer at Solaris Asset Management, told Bloomberg. "Draghi threw a degree of caution on the markets, but now people are waiting for tomorrow, absolutely."
US markets will be closed on Monday for a holiday.