Investors had been on a selling spree or have remained on the sidelines due to uncertainty because of Britain's Brexit vote.
Asian shares came within reach of testing their 2016 peak on Wednesday as prospects of solid US growth and accommodative economic policy in major markets whet investors' risk appetite damaged by uncertainty from Brexit.
MSCI's broadest index of Asia-Pacific shares outside Japan rose as much as 0.4% to 427.83, just below its year-to-date high of 428.22 hit on April 21.
Japan's Nikkei gained 1%. Australian stocks added 0.3% and South Korea's Kospi rose 0.6%. New Zealand shares were little changed, hovering near a record high struck Tuesday. Shanghai advanced 0.3%.
MSCI's broadest gauge of the world's stock markets has recovered all the losses after Britain's referendum to hit its highest level in over a month.
"A while ago, everything looked so uncertain on Brexit. But now the UK looks set to have a new prime minister and negotiations may begin earlier. That is soothing investor sentiment," said Masahiro Ichikawa, senior strategist at Sumitomo Mitsui Asset Management.
Britain's interior minister Theresa May is set to take over as the country's prime minister on Wednesday.
On Wall Street, S&P 500 gained 0.7% to a new record close of 2,152.14 while the Nasdaq turned positive for the year. Friday's robust jobs data has bolstered views that the US economy is on solid footing despite a slow start to the year.
European bank shares, seen as one of the weakest links in the global economy, rose as Italy moved closer to a deal with the EU executive to safeguard its struggling banks.
In Japan, Prime Minister Shinzo Abe ordered a new round of fiscal stimulus spending after an election victory.
His meeting on Tuesday with former US Federal Reserve Chair Ben Bernanke, a proponent of "helicopter money" policies - printing money and directly handing it to the private sector to stimulate the economy - fuelled speculation Abe's stimulus could be funded by the Bank of Japan's easing.
Such expectations pushed down the yen 4% over the last two days. The yen last traded at 104.23 yen to the dollar .
Elsewhere, the Bank of England makes its policy announcement on Thursday, with some players expecting a rate cut.
The European Central Bank is also widely expected to take a dovish stance when it holds its policy review a week later.
"After being faced with the prospect of a major slowdown in global activity in the wake of the Brexit vote, governments and central banks worldwide are now expected to do their utmost to reassure markets and provide stimulus," wrote Angus Nicholson, market analyst at IG in Melbourne.
"This has led to an incredible rally in equities and industrial commodities. Of course, should those expectations fail to eventuate they could stop the rally short. The greatest unknown for markets is what will happen in mainland Europe."
The British pound traded at $1.3270 after surging almost two% on Tuesday, pulling away from a 31-year low of $1.2798 struck late in June, as investors bought back the currency on May's appointment as prime minister.
The euro was little changed at $1.1060.
In commodities, oil prices dropped after industry group American Petroleum Institute (API) reported a surprise build of 2.2 million barrels in US crude stockpiles last week.
Brent crude futures fell 0.9% to $48.01 after surging roughly 5% on Tuesday on broad improvement in risk sentiment.
Zinc touched a 13-month high of $2,209 a tonne and nickel climbed to a 10-month peak of $10,580 a tonne. Aluminium and copper have also gained.
In Asia, one key focus is Chinese trade data later in the day, which will come ahead of China's GDP data on Friday.
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