The S&P/ASX200 jumped 146.2 points by midday, up 1.72 per cent, to 8,629, as the broader All Ordinaries gained 156.9 points, or 1.81 per cent, to 8,840.8.
The local rally followed a strong Wall Street session, when Mr Trump flagged the US military campaign could end "within two weeks, maybe two weeks, maybe three".
While Mr Trump has promised an end to the conflict on multiple occasions, his latest comments appeared the most definitive to date, Betashares chief economist David Bassanese said.
"Trump's final calculation appears relatively straightforward," Mr Bassanese said.
"US boots on the ground, or significant damage to civilian energy infrastructure, would likely push oil prices to $US200, trigger a US recession, and potentially lead to Democratic control of Congress and impeachment proceedings against Trump."
While questions remain about freeing up the Strait of Hormuz, a choke point for a fifth of global oil shipments, an end to the conflict could help the world avoid a recession in the nick of time, Mr Bassanese said.
Iran's leadership has also expressed a willingness to end the war, but its Revolutionary Guard has threatened to attack US businesses operating in the region.
Brent crude has eased from around $US108 a barrel to $US104.30, still up more than 40 per cent since the US campaign began on February 28.
The potentially improved outlook for global growth sent Australian investors flocking to basic materials stocks, the sector jumping 4.6 per cent by midday and tracking similar gains for mega miners BHP and Rio Tinto.
Beaten-down gold stocks performed even better, as the precious metal lifted to $US4,700 an ounce, boosting the All Ordinaries gold sub-industry by almost six per cent.
South32, PLS, Lynas Rare Earths and Sandfire Resources all rallied around four per cent or more.
Hopes of an end to the Middle East conflict supported ASX-listed airlines, with Qantas and Virgin Australia up more than 3.8 per cent each.
The big four banks led the heavyweight financials sector one per cent higher, with Westpac out front with a one per cent advance to $39.86.
As surging fuel prices continue to weigh on household budgets, the Australian Banking Association urged anyone struggling with loan repayments and budgeting to reach out to their bank for assistance.
Energy and utilities stocks were the weakest performers, slipping as Woodside, Origin and APA Group swung into the red.
Ampol and Viva Energy, the operators of Australia's two remaining fuel refineries, dipped 0.6 per cent and 2.9 per cent respectively.
Coal stocks were mixed, while uranium producers rebounded from recent weakness as the rosier global outlook sent names such as Paladin and Deep Yellow more than five per cent higher.
But even if the US ended its Iran campaign in a few weeks, it would take time for oil prices to normalise, meaning higher inflation, lower consumer spending and slow economic growth would likely persist, AMP deputy chief economist Diana Mousina said.
"Those fundamentals are mostly still intact, provided that the conflict doesn't drag out much beyond the next few weeks," she added.
"However, in the interim, bad news on negotiations, or more missile strikes are possible, which will send oil prices higher, and that could see another five-to-ten per cent hit on share markets."
Consumer-discretionary stocks bounced 1.1 per cent, following strong performances from Eagers Automotive on the back of a trading update, while Light & Wonder and Aristocrat also charged higher.
Investors bought up ASX-listed IT stocks at a discount, as the sector rebounded more than three per cent, although it's still trading on par with its value more than two years ago.
The Australian dollar was buying 69.28 US cents, up from 68.69 US cents on Tuesday.
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