The gains came ahead of the release of key US data that could provide a fresh idea about the Federal Reserve's plans for interest rates amid expectations the next president's tax and tariffs plans will reignite inflation, tempering rate cut bets.
Investors are also keeping tabs on the Ukraine and Middle East conflicts, which have helped push oil prices higher in recent weeks.
Investors gave the thumbs-up to news that US president-elect Trump had chosen billionaire investor Scott Bessent to lead the Treasury, with optimism he will take a considered approach to the economy.
Bessent, CEO of hedge fund manager Key Square Group, has called for an extension of tax cuts from Trump's first term. He also wants to reassert American energy dominance and believes it is necessary to deal with the budget deficit.
Recently, he has called for tax reform and deregulation to spur growth and wrote in a Wall Street Journal opinion piece that this would be key to "restarting the American growth engine" and keeping prices in check.
This month, he called tariffs "a negotiating tool with our trading partners" in an opinion piece for Fox News, adding it was "a means to finally stand up for Americans".
While his views are seen as hawkish, markets started on a bright note.
"(Bessent) brings this sense of almost gradualism to the administration as opposed to taking a big bang approach to making big policy changes," Brian Jacobsen, chief economist at Annex Wealth Management, told Bloomberg TV.
Markets may be relieved that the pick signals "an 'America First' kind of administration but not an 'America Exclusively' kind of administration", he added.
After a strong finish Friday on Wall Street -- where the Dow ended on a record -- Asian markets were broadly stronger.
Tokyo advanced more than one percent, even as the yen pushed up against the dollar, while Sydney, Seoul, Singapore, Taipei, Mumbai, Bangkok, Wellington, Manila and Jakarta also sat in positive territory.
However, after a healthy start, Hong Kong, Shanghai and Bangkok turned negative.
London, Paris and Frankfurt rose at the open.
Bitcoin sat at around $98,000, having set a record high of $99,728.34 on Friday, with traders awaiting the next catalyst to push it past the $100,000 mark.
The digital currency has bounded about 50 percent higher since Trump's election at the start of the month, with hopes he will usher in measures to ease restrictions on it.
Attention this week will be on a series of releases out of Washington that could sway US central bankers ahead of their next rate decision in December.
Among the key points of interest are the Fed's preferred gauge of inflation, minutes from the bank's most recent policy meeting, economic growth, and jobless claims.
Oil prices dipped after a recent run-up fuelled by concerns over Israel's ongoing wars with Hamas and Hezbollah, as well as Russia's decision to hit Ukraine with a new-generation intermediate-range missile that ramped up tensions with the West.
- Key figures around 0810 GMT -
Tokyo - Nikkei 225: UP 1.3 percent at 38,780.14 (close)
Hong Kong - Hang Seng Index: DOWN 0.4 percent at 19,150.99 (close)
Shanghai - Composite: DOWN 0.1 percent at 3,263.76 (close)
London - FTSE 100: UP 0.5 percent at 8,301.95
Euro/dollar: UP at $1.0464 from $1.0418 on Friday
Pound/dollar: UP at $1.2584 from $1.2530
Dollar/yen: DOWN at 154.15 yen from 154.83 yen
Euro/pound: UP at 83.15 pence from 83.11 pence
West Texas Intermediate: DOWN 0.9 percent at $70.59 per barrel
Brent North Sea Crude: DOWN 0.8 percent at $74.54 per barrel
New York - Dow: UP 1.0 percent at 44,296.51 (close)
dan/lb
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