At the close on Thursday the S&P/ASX 200 index had picked up 26.8 points, or 0.3 per cent, to 8226.3 points.
The broader All Ordinaries finished 25.6 points higher, or 0.3 per cent, at 8481.6.
US equities climbed, the greenback shot higher and bond yields surged as the Republican former president defeated Democratic candidate Kamala Harris in the election.
Moomoo Australia market strategist Jessica Amir said investors appeared to be buying "every and any risk asset that could benefit from Trump's pro-business, low-regulation, low-tax stance".
"For the most part, stocks and risk assets should perform strongly over the coming weeks and months, with the US Federal Reserve expected to cut rates for the second time this year on Friday, ahead of what could be a gangster 'Santa rally'," she said.
Senior Reserve Bank of Australia officials told a parliamentary hearing on Thursday the US president-elect's policies could have an adverse impact on the Australian economy but it was too early to judge the full implications.
Five of the 11 ASX 200 sectors posted gains, led by energy stocks, with Woodside lifting 3.2 per cent and Santos 2.4 per cent.Â
The interest rate-sensitive real estate sector performed poorly, reflecting the potential for Trump's tariff and immigration proposals to keep inflation and interest rates higher.
National Australia Bank shares wobbled after posting a lower profit than the year prior, but still ended the day a touch higher, up 0.2 per cent to $39.33.
Other big banks were mixed, with CBA up 1.2 per cent, to $147.26, and ANZ posting a 1.4 per cent gain, to $31.71.
Westpac fell 2.3 per cent, to $31.51.
Materials finished higher despite a drag from gold stocks as the metal's price declined, with Evolution Mining sinking 6.5 per cent and Northern Star down 6.3 per cent.
But index heavyweights were higher, with Fortescue up 3.3 per cent, to $19.50, Rio Tinto growing 1.9 per cent, to $121.66, and BHP logging a 0.9 per cent improvement, to $42.99.
Shares of Sigma Healthcare surged 24.9 per cent to a record high of $24.30 as the Australian Competition and Consumer Commission approved the $8.8 billion merger with pharmacy business Chemist Warehouse.
ON THE ASX:
* At the close on Thursday the S&P/ASX 200 index had picked up 26.8 points, or 0.3 per cent, to 8226.3 points.
*The broader All Ordinaries finished 25.6 points higher, or 0.3 per cent, at 8481.6.
CURRENCY SNAPSHOT:
One Australian dollar buys:
* 66.21 US cents, from 65.40 US cents at Wednesday's close.
*102.08 Japanese yen, from 100.43 Japanese yen.
*61.66 Euro cents, from 60.69 Euro cents.
*51.24 British pence, from 50.66 British pence.
*110.07 NZ cents, from 110.20 NZ cents.
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