Morrison spoke to reporters last night, saying he had conceded to Albanese.
"It's a difficult night for Liberals and Nationals around the country, as nights like this always are.
"They are humbling, but so is victory. Victory is also humbling and always should be.
"Tonight, I've spoken to the Leader of the Opposition and the incoming Prime Minister Anthony Albanese, and I've congratulated him on his election victory."
"I believe it's very important that this country has certainty. I think it's very important this country can move forward, and particularly over the course of this week with the important meetings that are being held in Tokyo, I think it's vitally important that there's a very clear understanding about the government of this country."
Morrison said he would step down as party leader at the next meeting.
While it remains unclear if Labor can form a majority, the ALP is on track to finish ahead of the Coalition and more likely to reach a minority government, the ABC projected earlier in the night.
"The Coalition cannot get into government," ABC election analyst Antony Green said.
New Prime Minister a parliament veteran
This win means Albanese will replace Scott Morrison as prime minister, making him the 31st person to hold the nation's top job.
The son of a single parent who grew up in public housing, Albanese has reached the pinnacle of his career after 26 years in the parliament.
Labor started the campaign, notionally, with 69 seats.
As of 10:30pm, the party looks set to make history by winning government from opposition despite going backwards on its national primary vote - down 2 per cent as of 10:30pm.
Crossbench and minor parties have experienced major gains, while the Coalition's primary vote is down more than 5 per cent.
The Liberal Party has suffered major losses to so-called "teal" independents, which look to take the seats of Mackellar, Goldstein, North Sydney. It also looks to suffer big losses in Western Australia.
Treasurer Josh Frydenberg looks to be one of the highest profile Liberal losers, telling supporters at 10pm that his path to re-election looked tough.
"So while it's mathematically possible that we win Kooyong, it's definitely difficult," he said.
Frydenberg was considered a frontrunner to lead the Coalition in opposition.
Labor has also picked up Liberal seats in Reid, in Sydney, and Chisholm, in Melbourne, while the Coalition has lost the seat of Ryan, in Brisbane, to the Greens.
But two Labor frontbenchers look to be in a fight to retain their seats, with Terri Butler in Griffiths, in Brisbane, and Senator Kristina Keneally, seeking to move to the Lower House seat of Fowler, in western Sydney, struggling to hold on.
Defence Minister Peter Dutton is holding his seat and becomes one of the most likely contenders to be the next Liberal leader.
"We have, as a Liberal family, suffered a terrible day today," he said.
"There are colleagues around the country, good people, who have potentially lost their seats."
Finance Minister Simon Birmingham said his Liberals needed to take stock from the swings it was seeing against it in once-safe seats.
"It is a clear problem that we are losing seats that are heartland seats, that have defined the Liberal Party for generations," he said.
"And so, if we lose those seats, it is not certain that we will, but there is clearly a big movement against us and there is clearly a big message in it, and we need to heed that message."
Senator Birmingham said his party "absolutely" needed to pre-select more women but feared that effort could be even harder with the loss of first-term female MPs Katie Allen, Fiona Martin and Celia Hammond.
Photo AFP Caption: Opposition Leader, Anthony Albanese greets supporters at a polling station during Australia's general election in the suburb of Carnegie in Melbourne on May 21, 2022