The benchmark S&P/ASX200 index was up 49.1 points, or 0.58 per cent, to 8,451.5 while the broader All Ordinaries was up 49.5 points, or 0.57 per cent, to 8,701.9.
Moomoo market strategist Jessica Amir said that stocks, crypto assets and gold were on "cloud nine" after Trump's first day in office.
But the US dollar had slipped against a basket of six other currencies as markets awaited certainty about Trump's tariff plans.
Trump told reporters overnight that his team was discussing 10 per cent tariffs on China, far less than the 60 per cent levies he had threatened on the campaign trail.
The new commander-in-chief also unveiled a $US500 billion AI joint venture between OpenAI, Oracle and SoftBank dubbed "Stargate".
ASX uranium miners gained on the news, as traders bet the AI strategy would mean an increased role for nuclear energy to power the power-hungry AI data centres.
Boss Energy, Paladin and Deep Yellow were the top three gainers among the ASX200, rising 14.2, 10.1 and 7.9 per cent respectively.
Paladin's gains also came as the uranium developer said production at its Langer Heinrich mine in Namibia was on track to meet revised guidance.
Overall, four of the ASX's 11 sectors closed lower and seven finished higher.
Tech was the biggest gainer, rising 2.4 per cent as Life360 added 3.4 per cent and Xero climbed 2.4 per cent.
Sentiment in the sector was boosted by Netflix, whose shares soared by 14.4 per cent in after-hours Nasdaq trading as the streaming giant blew out expectations by adding 18.9 million paid subscribers in the fourth quarter - the most in its history.
In the ASX's heavyweight mining sector, Iluka slid 7.0 per cent to $4.95 after the mineral sands miner said it would cut about 130 roles across its operations and support functions to save costs.
Elsewhere in the sector, BHP dropped 2.0 per cent to $39.80 after the Big Australian reported a 10 per cent rise in copper production, while Fortescue slid 0.8 per cent to $119.61 and Rio Tinto dropped 1.8 per cent to $19.03 amid Trump's tariffs talk.
Goldminers mostly rose as the precious metal changed hands at $US2,755 an ounce, its highest level since late October.
Regis advanced 2.7 per cent while Evolution rose 4.1 per cent as the goldminer reported record quarterly cash flows of $165 million, up 54 per cent from the quarter before.
In the energy sector, Woodside dropped 1.9 per cent to $25.25 as Australia's biggest oil and gas producer announced its fourth-quarter revenue was down six per cent to $3.47 billion.
Carnavon Energy fell 4.2 per cent to 11.5 cents after its joint venture partner Santos decided not to proceed with plans to buy an oil production vessel and not to start engineering and design work on its $3 billion-plus Dorado project off the coast of Western Australia.
In the financial sector, all of the big four banks finished higher with Westpac adding 0.7 per cent to $32.98, ANZ climbing 0.2 per cent to $30.22 and CBA and NAB both advancing 1.0 per cent to $157.75 and $39.26 respectively.
The Australian dollar was approaching a fresh two-week high, buying 62.65 US cents, from 62.37 US cents at close of business Tuesday.
ON THE ASX:
* The benchmark S&P/ASX200 index on Wednesday rose 27.4 points, or 0.33 per cent, to 8,429.8
* The broader All Ordinaries gained 27.8 points, or 0.32 per cent, at 8,680.5
CURRENCY SNAPSHOT:
One Australian dollar buys:
* 62.65 US cents, from 62.37 at close of business Tuesday
* 97.64 Japanese yen, from 96.93 yen
* 60.15 euro cents, from 60.09 euro cents
* 50.76 British pence, from 50.80 pence
* 110.68 NZ cents, from 110.53 NZ cents
Bitcoin was trading for $A167,724, up 3.0 per cent in the past 24 hours
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