At 10:30 (AEST), the benchmark S&P/ASX 200 was up 79.90 points or 1.55 percent at 5,234.20, while the broader All Ordinaries index was up 81.80 points or 1.58 percent at 5,270.50.
The energy sector was over 8 percent higher in early trade, while the rest of the market posted more modest improvements.
Last month the sector took the biggest hit from combined COVID-19 concerns and moves by large oil producing companies, however latest developments saw a sharp rise in the commodity price sending stocks into overdrive.
"Crude oil prices jumped by 25 percent after (U.S.) President (Donald) Trump tweeted that he'd brokered a deal with Saudi Arabia and Russia to cut production," CMC Markets Chief Market Strategist Michael McCarthy said.
"Surging energy stocks lifted share markets to positive territory despite the global count of COVID-19 infected rising through 1 million."
In the financial space, Australia's big banks lifted with the Commonwealth Bank up (1.27 percent), ANZ up (0.50 percent), National Australia Bank up (1.25 percent) and Westpac Bank up (0.75 percent).
Mining stocks rallied with Rio Tinto up (3.62 percent), BHP up (3.69 percent), Fortescue Metals up (5.11 percent), and goldminer Newcrest up (2.30 percent).
The country's oil and gas producers surged with Oil Search up (18.77 percent), Santos up (13.35 percent) and Woodside Petroleum up (8.81 percent).
Australia's largest supermarkets were mixed with Coles up (0.62 percent), and Woolworths down (0.67 percent).
Meanwhile telecommunications giant Telstra rallied (0.48 percent), the national carrier Qantas lifted (1.56 percent) and biomedical firm CSL jumped (1.19 percent).
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