The $528 million inquiry, which will be headed by Justice Ronald Sackville and based in Brisbane, will examine mistreatment across institutions, workplaces, schools, homes and the wider community.
Justice Sackville will be supported by five other commissioners, some of whom have lived experience of disability.
The three-year royal commission will look both backwards and forwards, and investigate the National Disability Insurance Scheme.
Mr Morrison said people with disabilities were much more likely to suffer abuse, violence, neglect and exploitation.
"People living with disability have faced the most difficult of circumstances because of their own condition," he said.
"But worse than that is the lack of a culture of respect towards people with disability that leads to their abuse and mistreatment.
"We have to establish a culture of respect for people living with disabilities and the families who support, love and care for them."
An emotional Mr Morrison quoted his brother-in-law Gary, who has multiple sclerosis, while announcing details of the royal commission.
"As my brother-in-law Gary said to me, it is not flash being disabled, but the good thing is that that's the condition you live with in Australia and that you're an Australian," he said, pausing to clear his throat.
"That has always meant a lot to me. They deserve our respect. This is so above politics I can't tell you.
"To all those Australians with a disability, their families, to Gary, this is for you."
More than 3700 people responded to public consultation on the terms of reference.
The royal commission will hand down a final report in April 2022.
But Mr Morrison said if the six royal commissioners need more time, they would receive it.
"This is a no limits inquiry," he said.
Opposition Leader Bill Shorten promised to adhere to the funding and scale of the commission should Labor win the coming federal election.
"This is what we wanted and if the government's not being stingy about the roll out of it - fine," he told reporters in Canberra.
Greens senator Jordon Steele-John, who was a leading advocate for the commission, is proud it is coming to fruition after years of campaigning.
"We are dying in our homes, in our workplaces, in our educational spaces. We are being raped, we are being starved, we are being beaten," the senator told ABC News.
However, Senator Steele-John is disappointed there is no mention of redress in the terms of reference.
He also says two of the commissioners with previous responsibilities in the disability sector, John Ryan and Barbara Bennett, were "good people" but should not be involved because of potential conflicts of interest.
A spokeswoman for Social Services Minister Paul Fletcher said the pair had received Australian honours for their significant contribution in their fields.
"Any suggestions as to the validity of their appointment is without foundation."