MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.15% while Japan's Nikkei share average gained 0.7% to hit one-month high.
Investors took their cue from upbeat US hosing data on Friday, with sales of new single-family homes rising more than expected in April and the number of houses on the market hitting a 3-1/2 year-high.
The figures were good enough to boost Wall Street shares after Federal Reserve chief Janet Yellen said earlier this month that a slumping housing market, as well as geopolitical tensions, risked undermining the US economy
The S&P 500 index closed at a record high of 1900.53 on Friday, just below a record intraday high of 1,902.17 set on May 13, buoyed by a rally in housing stocks.
"Looking at housing shares, you could say markets had already lowered expectations on the housing markets sharply," said Tohru Yamamoto, chief strategist at Daiwa Securities.
"Last month, investors were expecting a sharp rebound after a bad weather. But if you think housing is a downside risk, the figures look pretty good," he said.
Investors were also hoping for easing geopolitical risks after exit polls in Ukraine gave Poroshenko, a confectionery magnate with long experience in government, more than 55% of the vote in the presidential election.
Results will not be announced until later on Monday but runner-up Yulia Tymoshenko, on 13%, made clear she would concede, sparing the country a tense three weeks until a runoff round would have been held.
"Poroshenko's victory in the first round of vote is positive for political stability, even though there remains a huge uncertainty and we need to keep an eye on further developments," said Junya Tanase, chief currency strategist at JPMorgan Chase Bank in Tokyo.
Market holidays in London and New York on Monday may curb activity in Asia.
The improved mood put pressure on the safe-haven yen, which fetched 101.97 yen to the dollar in early trade, near its lowest level in more than a week.
The euro faced pressures of its own, holding near a three-month low of $1.3615, not helped by a rise in votes for anti-establishment parties in the European Parliament elections, especially in France and Greece.
In France, the far right National Front scored a stunning victory, forcing French Prime Minister Manuel Valls to call the breakthrough by the anti-immigration, anti-euro party "an earthquake" for France and Europe.
Greece's radical leftist Syriza also rode a wave of anti-austerity anger to win the country's EU election, though it failed to deliver a knockout blow against Prime Minister Antonis Samaras's government, the official projection showed on Sunday.
"We have to pay attention to how periphery euro bonds will react to the election results. Because their spreads have been tightening sharply over the past year, there could be some correction, in which case the euro could face further pressure," said JPMorgan's Tanase.
The common currency has fallen 1.7% so far this month, pressured by European Central Bank President Mario Draghi's suggestion earlier this month that the bank will adopt stimulus at its next policy meeting in June.
Disappointing German business sentiment data on Friday reinforced expectations of an imminent ECB policy easing.