At the market close, the benchmark S&P/ASX 200 index was up 189.70 points or 4.17 percent at 4,735.70, while the broader All Ordinaries index was up 189.20 points or 4.15 percent at 4,753.3.
"Aussie shares rallied in late trade to finish at intraday highs following signs of a firmer start on Wall Street tonight," Commsec market analyst Steven Daghlian said.
However, he reminded the local stocks slumped by 6 percent on Monday, "the index remains near a 2012 low and the ASX 200 is still down by almost 35 percent in just 23 day".
All sectors finished higher on Tuesday with gains from the recently heavily sold of banks, property stocks and materials helping most.
In the financial space, Australia's big banks jumped with the Commonwealth Bank up (5.05 percent), ANZ up (5.32 percent), National Australia Bank up (3.75 percent) and Westpac Bank up(2.91 percent).
Mining stocks rallied with Rio Tinto up (1.07 percent), BHP up (5.07 percent), goldminer Newcrest up (6.51 percent) and Fortescue Metals up (1.89 percent).
The country's oil and gas producers surged with Oil Search up (8.51 percent), Santos up (20.55 percent) and Woodside Petroleum up (5.63 percent).
Australia's largest supermarkets were mixed with Coles up (3.59 percent), and Woolworths down (0.74 percent).
Meanwhile telecommunications giant Telstra bounced (2.27 percent), the national carrier Qantas soared (7.75 percent) and biomedical firm CSL lifted (1.10 percent).
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