The S&P/ASX 200 index rose 0.3 percent, or 18.3 points, to 6,079.1 at the close of trade. The benchmark had edged 0.2 percent lower on Monday.
Shares of Australia's largest investment bank rose 2.1 percent to a more than four month closing high after the firm said it remained on track for a record annual profit.
Meanwhile, shares of biotherapeutics heavyweight CSL Ltd strengthened 1.6 percent ahead of its half yearly results scheduled to be released on Wednesday.
New Zealand's benchmark S&P/NZX 50 index posted its fifth straight session of gains, rising 0.8 percent or 70.77 points to finish the session at 9,280.77. The New Zealand-listed shares of Australia and New Zealand Banking Group Ltd rose 1.3 percent, while those of Goodman Property Trust gained 2.2 percent.