It will be led by former NSW Supreme Court judge Ronald Sackville, who will be assisted by five other commissioners, some of whom have lived experience of disability.
The government voted in favour of setting up the royal commission only after a motion calling for the commission was put forward by Greens Senator Jordon Steele-John and passed with Labor's support in February.
The inquiry is set to examine the mistreatment in institutional settings, workplaces, schools, home and the community.
"The royal commission will inquire into all forms of violence, abuse, neglect and exploitation. It will cover all settings in which these abuses occur - all settings," Mr Morrison told reporters on Friday morning.
It's the sixth royal commission in six years.
Mr Morrison became emotional as he talked about his brother-in-law Garry, who has multiple sclerosis.
"As my brother-in-law Garry also 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.
"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 Garry, this is for you."
Both major parties had asked if states and territories would be willing to share the cost, but have now committed to fully funding it.
While previously allocating only $26 million to the commission, Opposition Leader Bill Shorten said on Friday that Labor would match the spending commitment to ensure the inquiry goes ahead.