Platforms such as Facebook, TikTok and Instagram would be held responsible for enforcing the age ban, Albanese said, and face potentially hefty fines for failing to do so.
The Australian government first mooted a social media age limit earlier this year, and the idea enjoys broad bipartisan support among lawmakers.
"This one is for the mums and dads. Social media is doing real harm to kids and I'm calling time on it," Albanese said.
The new laws would be presented to state and territory leaders this week, before being introduced to parliament in late November.
Tech platforms would then be given a one-year grace period to figure out how they would implement the ban.
Albanese said unchecked social media algorithms were serving up disturbing content to highly impressionable children and teenagers.
"I get things popping up on my system that I don't want to see. Let alone a vulnerable 14-year-old," he said.
"Young women see images of particular body shapes that have a real impact."
Albanese said he had settled on 16 as an appropriate age after a series of age verification trials conducted by the government.
Analysts have previously expressed doubt that it would be technically possible to enforce such a strict age ban.
- 'Truly world-leading' -
"We already know that present age verification methods are unreliable, too easy to circumvent, or risk user privacy," University of Melbourne researcher Toby Murray said earlier this year.
A series of exemptions would be decided for platforms such as YouTube, which teenagers may need to use for school work or other reasons.
Australia has been at the vanguard of global efforts to clean up social media.
The government introduced a "combating misinformation" bill earlier this year, outlining sweeping powers to fine tech giants for breaching online safety obligations.
Australia's online watchdog is locked in a running battle with Elon Musk's X, accusing the platform of failing to stamp out harmful posts.
Communications Minister Michelle Rowland said the reforms were "truly world-leading".
Social media platforms were repeatedly "falling short", she said at Wednesday's press briefing with Albanese.
"Social media companies have been put on notice," Rowland said.
"They need to ensure their practices are made safer."
Rowland flagged that there would be financial penalties for tech companies that failed to comply.