The local currency was quoted at 1,097.4 per dollar at the end of onshore trade on Tuesday, compared with 1,103.3 on Monday.
Benchmark 3-year bond futures for March delivery surged 18 basis points to 108.87, extending gains after the RBA's rate cut triggered bets that South Korea's central bank could be pressured to follow suit by easing policy as well.
South Korean shares closed nearly flat on Tuesday, as easing worries over Greece's future in the euro zone were offset by slowing global growth and deflationary concerns.
The Korea Composite Stock Price Index (KOSPI) ticked 0.04 percent lower to close at 1,951.96 points.