Morrison's emotional speech given in Parliament before hundreds of survivors followed the conclusion of a Royal Commission into Institutional Responses to Child Sexual Abuse, the nations' highest level of inquiry.
"Today as a nation we confront our failure to listen, to believe, and to provide justice," he said, adding: "We say sorry."
Abuse survivors gathered in Parliament's Great Hall cried, yelled and applauded as Morrison read the apology.
"I believe you, we believe you, your country believes you," he said.
The four-year inquest that delivered its final report in December revealed shocking evidence from more than 17,000 survivors and heard allegations against government, church and private institutions, as well as prominent individuals.
It also heard evidence from leaders such as Vatican Cardinal George Pell, who is charged with committing historical sex abuses himself and was accused of failing to protect children.
The prime minister said in his speech Monday that it was time for Australia to confront key questions.
"Why weren't the children of our nation loved, nurtured and protected? Why was their trust betrayed?" he said.
"Why did those who know cover it up? Why were the cries of children and parents ignored? Why was our system of justice blind to injustice? Why has it taken so long to act? Why were other things more important than this, the care of innocent children? Why didn't we believe?"
Morrison said nothing could be done to right the wrongs inflicted on children.
"Even after a comprehensive royal commission, which finally enabled the voices to be heard and the silence to be broken, we will all continue to struggle," he said.
"So today, we gather in this chamber in humility, not just as representatives of the people of this country, but as fathers, as mothers, as siblings, friends, workmates and, in some cases, indeed, as victims and survivors."
The lawmakers stood for a minute of silence following the apology, which came with the announcement of government plans to create a museum and research center to raise awareness and understanding of the impacts of child sexual abuse, and to ensure the nation does not forget the horrors victims have suffered.
The research center will also assist those seeking help, and guide best practices for training and other services.
The government will also commit to reporting every year for the next five years on the progress of the royal commission's recommendations.
It has already accepted 104 of the commission's 122 recommendations, including a redress payments program, with the other 18 recommendations still under examination.
The government has also established a new office of child safety, to report to the prime minister.
Opposition leader Bill Shorten joined the apology, saying Australia had failed tens of thousands of children, across generations.
"Our nation let you down. Today, we offer you our nation's apology, with humility, with honesty, with hope for healing now, and with a fire in our belly to ensure that our children will grow up safe in the future," Shorten said.
While many survivors and campaigners welcomed the apology, others called for more to be done to address the history of abuse.
In Canberra, Rick Venero, who was abused at a Marist Brothers school in Sydney, said action should be taken against institutions that protected pedophiles.
"(The apology) meant a great deal. It's fantastic to get that from the Australian people," Venero said. "(But) it's pretty shattering actually, to come here and everyone's behind it, and the power of these institutions means that nothing's really happening."
Leonie Sheedy, chief executive of the Care Leavers Australia Network, which advocates for those raised in state care, called on the government to remove a charity tax exemption from institutions that are still deciding whether to opt in to the national redress program for victims.
She said she's never healed from being abused.
"You can learn to live with it, but it never goes away," Sheedy told the Australian Broadcasting Corp. "It will be with me and all care leavers until the day that they put the lid on the coffin."
