MSCI world equity index, which tracks shares in 45 countries, rose 0.8% near to 2016 highs after Federal Reserve Chair Janet Yellen urged caution on further rate hikes despite calls from some policymakers for faster progress.
The dollar fell across the board, with the dollar index down at 94.945, adding further losses to its biggest one-day fall in nearly two weeks seen on Tuesday.
The move also pumped up the euro to its highest level in almost two weeks and pulled Germany's 10-year bond yields -- the European benchmark -- towards record lows, as investors waited for inflation data that was likely to confirm the need for ultra-easy monetary policy in the bloc.
"Having had such seemingly unambiguous guidance from the other FOMC speakers where the message seemed to be very clearly to markets: you've taken this too dovishly, Yellen seemed to send the opposite message," said RBC Capital Markets' head of currency strategy in London, Adam Cole.
Futures markets dialed back their predictions of a rate hike to late 2016 from mid-year, in what some analysts warned might be a slight overreaction.
With the S&P 500 recording its highest close of the year, and Asian shares outside Japan reversing four sessions of losses to jump 2%, Europe followed the push higher.
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The pan-European FTSEurofirst 300 index advanced 1%. Britain's FTSE 100 rose 1.2%, Germany's DAX gained 0.7%, while the euro zone's blue-chip Euro STOXX 50 index rose 0.8%.
Japan's Nikkei was a rare loser, nudged lower by a rise in the yen against the dollar.
"We see the (Yellen) comments as an effort to exert control over the message and, in doing so, tilt expectations for policy rate hikes in a decidedly dovish direction," said Michael Gapen, chief US economist at Barclays.
Debt markets rallied hard in response to Yellen's speech, with yields on 10-year US paper dropping 7 basis points to a one-month low of 1.80%. German equivalents fell 2 bps to 0.13%, within a whisker of this year's low of 0.102% and an all-time low of 0.05% hit last year.
The drop in the US dollar helped oil prices regain a little ground, as did a forecast that US stockpiles may have grown by less than first thought.
US crude added 60 cents to $38.89 a barrel, after falling around 3% on Tuesday. Brent rose 40 cents to $39.60.
Gold was up at $1,242.66 an ounce, after rising almost 2% overnight.