The Aussie was last up 0.9% at $0.6926, having bounced from a four-month trough of $0.6865. It was briefly quoted as high as $0.6990 but dealers said that was a miss-hit and the actual transacted peak was $0.6938.
"The surprise victory is fuelling the rally as many expected the Labour party to win but an Australian rate cut is still very much on the cards in the coming months and that will weigh on the currency," said Esther Maria Reichelt, an FX strategist at Commerzbank in Frankfurt.
The centre-left Labor party had been tipped to win the federal election, beating Morrison's centre-right Liberal National Coalition, which investors see as more business-friendly.
Tepid economic data, including a rising jobless rate has stoked expectations the Australian central bank will cut interest rates as soon as July.
Elsewhere, the dollar held surprisingly firm on Monday, extending its gains from last week as concerns about a festering trade war between the United States and China burnished the safe-haven appeal of the greenback.
Positioning data offered a glimpse that the dollar strength may be tenuous, however, as investors have quietly trimmed some of their long positions in the U.S. currency against both its developed and emerging market rivals.
Against a basket of its rivals, the dollar steadied at a two-week high above 98.
The pound recouped some losses after posting its biggest weekly drop in six months last week, edging 0.2% higher at $1.2736 and 0.1% stronger against the euro at 87.62 pence.
Prime Minister Theresa May said on Sunday she would make a "new bold offer" to British lawmakers in an attempt to get her thrice-defeated Brexit deal through parliament before she leaves office.