The benchmark S&P/ASX200 index gained 65.6 points, or 0.79 per cent, to 8,318.4 on Tuesday, its first finish over 8,300.
The broader All Ordinaries gained 69.1 points, or 0.81 per cent, to 8,598.6.
The gains came after a strong lead from Wall Street, where the Dow Jones and S&P 500 hit another record high.
"While a clear catalyst for last night's rally was absent, the fundamental narrative is the same: the US economy is on solid footing, easier monetary policy and loose fiscal settings are waiting for market participants in 2024, and world-beating productivity is making it all possible by keeping inflation relatively contained," Capital.com analyst Kyle Rodda said.
IG market analyst Tony Sycamore said that there was also a sense of optimism about the Chinese economy following a dovish pivot from authorities there in late September.
The market seems to be assuming that fiscal stimulus measures were on the horizon, despite the current lack of specifics, Mr Sycamore said.
Nine of the ASX's 11 sectors finished higher, all except energy and consumer staples.
The heavyweight financial sector was the biggest gainer, rising 1.3 per cent.
CBA rose 1.8 per cent to $139.29, Westpac climbed 1.6 per cent to $31.56, NAB advanced 1.5 per cent to $38.18 and ANZ added 0.9 per cent to $31.15.
Eftpos providers Tyro Payments dropped 11.1 per cent to a four-month low of 80.5 cents and Smartpay Holdings plummeted 17.7 per cent to a two-year low of 70 cents after the Albanese government said it would ban debit card surcharging.
Both companies said they were engaged with the Reserve Bank about the issue.
"We support any review that assesses the true cost of card acceptance, including both debit and credit, for the fair regulation of payment acceptance in Australia," said Tyro chief executive and managing director Jon Davey.
In the heavyweight mining sector, BHP rose 0.5 per cent to $44.01, Fortescue added 2.3 per cent to $20.47 and Rio Tinto advanced 0.9 per cent to $122.07.
The energy sector was the laggard of the day, dropping 1.3 per cent after Brent crude slumped to a 12-day low of $US75 a barrel following a report Israel would refrain from targeting Iran's oil production facilities.
Woodside fell 2.2 per cent, Santos dropped 1.0 per cent and Whitehaven Coal dipped 0.8 per cent.
Uranium companies surged after Google signed a deal to purchase electricity from small modular reactor developer Kairos Power, as a means to power its energy-hungry AI data centres.
The first reactor will be online by 2030, with more by 2035.
Boss Energy rose 4.1 per cent, Paladin Energy advanced 2.4 per cent and Deep Yellow climbed 5.7 per cent.
The Australian dollar was at a one-month low against its strengthening US counterpart, buying 67.08 US cents, from 67.32 US cents at Monday's ASX close.
ON THE ASX:
* The benchmark S&P/ASX200 index finished Tuesday up 65.6 points, or 0.79 per cent, at 8,318.4
* The All Ordinaries gained 69.1 points, or 0.81 per cent, at 8,598.6.
CURRENCY SNAPSHOT:
One Australian dollar buys:
* 67.08 US cents, from 67.42 US cents at Monday's ASX close
* 100.28 Japanese yen, from 100.58 yen
* 61.61 euro cents, from 61.69 euro cents
* 51.43 British pence, from 51.59 pence
* 110.39 NZ cents, from 110.52 NZ cents
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