London closed the day 1.3 percent higher, Frankfurt won 1.4 percent and Paris surged 2.3 percent, with shares in French cosmetics giant L'Oreal soaring 6.7 percent on strong sales.
Wall Street also pushed higher, extending Tuesday's rally, with the Dow Jones Industrial Average climbing 1.2 percent in midday trading. The broader S&P 500 was up 1.3 percent and the tech-heavy Nasdaq Composite jumped 2.0 percent.
"No Halloween horrors as Red October draws to a close," concluded CMC Markets analyst Michael Hewson.
October has been a painful month for equities with sometimes massive losses and observers warn of further pain, with Washington and Beijing seemingly unlikely to back down from their tariffs stand-off anytime soon.
Europe's markets had faltered Tuesday, also on weak economic data and political uncertainty over Italy and Germany.
However, New York turned in a healthy performance Tuesday -- the Dow added 1.8 percent while the S&P 500 and Nasdaq jumped 1.6 percent -- after data showed US consumer confidence at a new 18-year high in October.
The positive tone woke up trades in Asia, where equities leapt Wednesday with attention also turning to the release of key US jobs data later in the week.
"There's been a strong rally in stock markets... as investors seek to recover from the recent declines," noted XTB analyst David Cheetham.
IG analyst Joshua Mahony noted however that "this bullish market sentiment comes despite a somewhat dour 24-hours for the global growth picture".
Chinese factory activity slowed in October, official data showed Wednesday. The Purchasing Managers' Index (PMI), a key gauge of factory conditions, came in at 50.2 for the month, just above the 50-point mark that separates expansion from contraction.
But analysts at Charles Schwab brokerage said "a string of upbeat earnings reports on both sides of the pond (are) helping offset lingering trade, Fed, and global growth uneasiness."
- Markets licking wounds -
Despite Wednesday's rally, a mountain of problems -- from China-US trade tensions and Brexit, to Chinese economic weakness and rising US interest rates -- have not gone away.
"Even after this morning's gains, global equity markets are left licking their wounds after a brutal month," noted Cheetham at XTB.
"Ongoing US-Chinese trade tensions, slowing global growth and rising US interest rates all have contributed to the sell-off and the question going forward now is whether the worst of it is over or if there's another wave of selling into year-end.
"The recent stabilisation is a pleasing development at least," he added.
The euro hit a fresh two-month low at $1.1305 on Wednesday. The dollar struck 6.9799 yuan, the highest level for a decade as the Chinese currency is pressured by US trade war fears.
Meanwhile, a strong jobs report out of Washington Friday could provide another reason for the US Federal Reserve to hike rates and put further upward pressure on the greenback.
Bitcoin, marking its 10th anniversary, rose to $6,309.89.