Partial results showed Morrison's Liberal-National coalition had been punished by voters in Western Australia and affluent urban seats in particular.
"Tonight, I have spoken to the Leader of the Opposition and the incoming Prime Minister, Anthony Albanese. And I've congratulated him on his election victory this evening," Morrison said, stepping down as leader of his party.
Labor had yet to reach the 76 of the 151 lower house seats required to form a government alone. Final results could take time as counting of a record number of postal votes is completed.
A strong showing by the Greens and a of group of so-called "teal independents," who campaigned on policies of integrity, equality and tackling climate change, means the makeup of the new parliament looks set to be much less climate-skeptic than the one that supported Morrison's pro-coal mining administration.