In a readout of the meeting, the U.S. State Department said discussions starting next year would focus on an open and transparent energy market.
Both sides said that "energy supply and security were issues of mutual interest that should be an ongoing item for bilateral discussion."
Formal negotiations are slated for the first half of next year. Clinton had said she would stand down as secretary of state for U.S. President Barack Obama's second term in office, which begins formally in January.
The State Department said Australia's role as a major energy supplier in the region was helping to stimulate economic growth in major Asian economies.
International energy companies like Chevron are exploring gas deposits in the country. Asian markets have secured long-term deliveries of liquefied natural gas from Australia in order to feed growing market demand.