The law will make platforms including TikTok, Facebook, Snapchat, Reddit, X and Instagram liable for fines of up to 50 million Australian dollars ($33 million) for systemic failures to prevent children younger than 16 from holding accounts.
The Senate passed the bill 34 votes to 19. The House of Representatives on Wednesday overwhelmingly approved the legislation 102 votes to 13.
The House has yet to endorse opposition amendments made in the Senate. But that is a formality since the government has already agreed they will pass.
The platforms will have one year to work out how they could implement the ban before penalties are enforced.
The amendments bolster privacy protections. Platforms would not be allowed to compel users to provide government-issued identity documents including passports or driver's licenses, nor could they demand digital identification through a government system.
The House is scheduled to pass the amendments on Friday. Critics of the legislation fear that banning young children from social media will impact the privacy of users who must establish they are older than 16.
While the major parties support the ban, many child welfare and mental health advocates are concerned about unintended consequences.
Sen. David Shoebridge, from the minority Greens party, said mental health experts agreed that the ban could dangerously isolate many children who used social media to find support.
"This policy will hurt vulnerable young people the most, especially in regional communities and especially the LGBTQI community, by cutting them off," Shoebridge told the Senate.
Opposition Sen. Maria Kovacic said the bill was not radical but necessary.
"The core focus of this legislation is simple: It demands that social media companies take reasonable steps to identify and remove underage users from their platforms," Kovacic told the Senate.
"This is a responsibility these companies should have been fulfilling long ago, but for too long they have shirked these responsibilities in favor of profit," she added.
Online safety campaigner Sonya Ryan, whose 15-year-old daughter Carly was murdered by a 50-year-old pedophile who pretended to be a teenager online, described the Senate vote as a "monumental moment in protecting our children from horrendous harms online."
"It's too late for my daughter, Carly, and the many other children who have suffered terribly and those who have lost their lives in Australia, but let us stand together on their behalf and embrace this together," she told the AP in an email.
Wayne Holdsworth, whose teenage son Mac took his own life after falling victim to an online sextortion scam, had advocated for the age restriction and took pride in its passage.
"I have always been a proud Australian, but for me subsequent to today's Senate decision, I am bursting with pride," Holdsworth told the AP in an email.
Christopher Stone, executive director of Suicide Prevention Australia, the governing body for the suicide prevention sector, said the legislation failed to consider positive aspects of social media in supporting young people's mental health and sense of connection.
"The government is running blindfolded into a brick wall by rushing this legislation. Young Australians deserve evidence-based policies, not decisions made in haste," Stone said in a statement.
The platforms had complained that the law would be unworkable, and had urged the Senate to delay the vote until at least June next year when a government-commissioned evaluation of age assurance technologies made its report on how young children could be excluded.
Critics argue the government is attempting to convince parents it is protecting their children ahead of a general election due by May. The government hopes that voters will reward it for responding to parents' concerns about their children's addiction to social media. Some argue the legislation could cause more harm than it prevents.
Criticisms include that the legislation was rushed through Parliament without adequate scrutiny, is ineffective, poses privacy risks for all users, and undermines the authority of parents to make decisions for their children.
Opponents also argue the ban would isolate children, deprive them of the positive aspects of social media, drive them to the dark web, discourage children too young for social media to report harm, and reduce incentives for platforms to improve online safety.