The S&P/ASX200 rose 81.8 points, or 1.04 per cent, to 7,925.2, while the All Ordinaries gained 73.7 points, or 0.92 per cent, to 8,126.9.
The performance came as the Reserve Bank of Australia confirmed expectations to hold the cash rate steady at 4.10 per cent, but concerns about a tight labour market and incoming US tariffs led analysts to marginally reduce bets on a May cut.
"The question we're asking ourselves is what (tariffs) might do to activity globally and inflation in Australia as we move on," RBA chair Michelle Bullock told reporters in Sydney.
"If the impact of tariffs on supply dominates, then you might see a rise in inflation, but it's also possible that trade diversion might end up with cheaper goods coming into Australia."
The central bank's policy decision statement concluded inflation risks to both supply and demand sides had left the board "cautious about the outlook".
All 11 local sectors finished higher, led by a 2.2 per cent rally in interest rate-sensitive real estate stocks and a 1.9 per cent lift in the traditionally defensive utilities sector.
A bounce in materials stocks helped lift the bourse higher after a sharp sell off on Monday, with iron ore giants BHP and Fortescue leading the charge, up 1.8 per cent each.
Rio Tinto didn't soar quite as high, gaining 1.4 per cent, after Norway's sovereign wealth fund announced it would oppose a review of the miner's dual listings in London and Sydney.
Financial stocks pushed 0.9 per cent higher after a weak start, with CBA and ANZ notching more than 1.3 per cent gains, as NAB lifted 1.1 per cent and Westpac traded flat despite a more than 85 million share buyback on Monday.
Telecommunications services and IT stocks also rallied, gaining 1.7 per cent and 1.5 per cent respectively after selling off significantly over late February and March.
Energy stocks rallied one per cent, led by 1.7 per cent gains for oil and gas giants Woodside and Santos, which were helped by a three per cent lift in oil prices overnight after US President Donald Trump chided Russia and Iran.
US manufacturing data is due overnight, with analysts expecting a slight contraction in activity over March.
Mr Trump's much-awaited "Liberation Day" tariff launch is looming, so investors could be tentative ahead of the president's announcement, which isn't expected until after midnight on Wednesday AEDT.
The Australian dollar is buying 62.56 US cents after an overnight sell-off and post-RBA meeting volatility, down from 62.81 on Monday at 5pm.
ON THE ASX:
* The benchmark S&P/ASX200 index gained 81.8 points, or 1.04 per cent, to 7,925.2
* The broader All Ordinaries rose 73.7 points, or 0.92 per cent, to 8,126.9
CURRENCY SNAPSHOT:
One Australian dollar buys:
* 62.56 US cents, from 62.81 US cents on Monday
* 93.74 Japanese yen, from 93.62 Japanese yen
* 57.89 euro cents, from 57.99 euro cents
* 48.43 British pence, from 48.49 British pence
* 110.25 NZ cents, from 110. 02 NZ cents
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