The S&P/ASX200 rose 48.2 points, or 0.58 per cent, to 8,343.3 as the broader All Ordinaries gained 48.6 points, or 0.57 per cent, to 8,573.4.
The RBA announced it would reduce the cash interest rate by 25 basis points to 3.85 per cent, its lowest level in two years.
Just before the decision, the top 200 was up 0.35 per cent and the All Ordinaries 0.33 per cent in the green.
As local shares pushed higher, VanEck Head of Investments and Capital Markets Russel Chesler warned premature rate cuts could lead to a resurgence of inflation.
"That said, rate cuts are generally good for markets, as it reduces the cost of capital and thus encourages business growth – particularly for small caps, which are typically more leveraged," he said.
"The additional rate easing, while mild, suggests business input costs should improve ... which is beneficial for mid- and small-caps that tend to have lower pricing power relative to larger companies."
Reserve Bank Governor Michele Bullock said while the board had been confident in its decision, global growth uncertainty was an ongoing concern.
"I would say that we are still not sure that the financial markets will remain nice and steady," Ms Bullock said.
"The key point about the situation we're in is it's not just uncertain, it's actually unpredictable."
Eight of 11 local sectors made gains as IT stocks (+2.3 per cent), real estate (+1.4 per cent) and telecommunications stocks (+1.2 per cent) rallied, while utilities, energy stocks and the materials sector edged lower.
Financials helped lift the bourse, rising 0.8 per cent as the Commonwealth Bank hit an intraday high of $173.54 before settling at $172.43, not quite pipping Friday's record daily close.
NAB and ANZ both rose by one per cent or more, Westpac edged 0.4 per cent higher and Macquarie Group shares rallied two per cent to $208.09.
The mining sector had a lethargic day of trade, with large cap miners BHP, Rio Tinto and Fortescue edging lower as iron ore futures held just above $US100 a tonne.
Gold miners sold off as risk-on sentiment pushed investors away from the safe haven, which is trading at around $US3,219 ($A5,008).
Energy stocks edged 0.2 per cent lower, tracking with an easing oil price as Brent Crude futures lost 22 US cents to trade at $US64.80 a barrel.
The Australian dollar sold off against major currencies after the rate cut announcement but recovered to trade at 64.16 US cents, up slightly from 64.12 US cents on Monday at 5pm.
Following the RBA decision, interest rate markets are pricing a 57 per cent chance of a July rate cut and have priced a total of 65 basis points of cuts between now and the end of the year.
This would leave the cash rate at 3.20 per cent heading into 2026.
ON THE ASX:
* The benchmark S&P/ASX200 index finished Tuesday 48.2 points higher, up 0.58 per cent to 8,343.3
* The broader All Ordinaries gained 48.6 points, or 0.57 per cent, to 8,573.4
CURRENCY SNAPSHOT:
One Australian dollar buys:
* 64.16 US cents, from 64.12 US cents on Monday at 5pm
* 92.70 Japanese yen, from 92.97 Japanese yen
* 58.98 Euro cents, from 57.20 Euro cents
* 47.97 British pence, from 48.13 pence
* 108.38 NZ cents, from 108.76 NZ cents
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