Safe-haven assets and currencies like gold, government bonds and the yen retreated.
MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS rose 1.3 percent.
"Those who were risk averse are reversing their positions," said Yoshinori Shigemi, global market strategist at JPMorgan Asset Management in Tokyo.
"Sentiment was extremely negative last week, but it's recovering now, though we should not be overly optimistic."
Japan's Nikkei soared to a one-week high on Monday, posting the biggest daily gain in two months as Brexit worries receded somewhat after weekend polls showed the campaign to keep Britain in the European Union regaining momentum.
The safe-haven yen weakened on the uptick in risk appetite and helped lift the Nikkei share average 2.3 percent to 15,965.30, the highest closing level since June 13. The index posted the biggest daily percentage gain since April 21.
China's main stock indexes were flat on Monday, bucking the upward trend in Asian markets, as sentiment was subdued amid concerns of yuan depreciation and a fresh regulatory crackdown on speculative trading.
Both the blue-chip CSI300 index and the Shanghai Composite Index rose just 0.1 percent, to 3,112.67 points and 2,888.59 points, respectively.
On Monday, other Asian markets had solid gains on hopes Britain will decide to remain in the European Union.
Hong Kong stocks jumped nearly 2 percent on Monday, their biggest one-day gain in almost a month, as Asian markets rebounded on hopes Britain will decide to remain in the European Union.
The Hang Seng index rose 1.7 percent, to 20,510.20, while the China Enterprises Index gained 1.8 percent, to 8,639.51 points.
Brexit fears abated as three British opinion polls ahead of the EU membership referendum on June 23 showed the "Remain" camp recovering some momentum, although the overall picture remained one of an evenly split electorate.
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