It acknowledges the suffering caused to thousands of people who were abused in children's homes and other residential institutions.
Victims and survivors groups have been critical of the time it has taken to get to this point, nine years after it was recommended by Sir Anthony Hart, chair of the Historical Institutional Abuse (HIA) Inquiry.
His 2017 report also recommended a public apology and compensation scheme, both of which have already been implemented, but some institutions criticised by the public inquiry have not yet made redress payments.
The Stormont memorial takes the form of a plaque in the entrance hall at Parliament Buildings.
Dozens of survivors attended the event on Friday.
'A black mark against the state'
Northern Ireland First Minister Michelle O'Neill said in her address that there "is no ambiguity about the failures which have occurred or the responsibility owed".
She said the memorial would stand "as a permanent acknowledgement and reminder that children were failed by the state and by others who had a duty to protect them".
Deputy First Minister Emma Little-Pengelly said: "We cannot change the past, but we can face it with honesty and integrity."
She told survivors and their families: "We are all so deeply sorry that you were failed by so many people for so long."
The speaker of the devolved assembly, Edwin Poots, said the abuse would "forever be a black mark against the state of Northern Ireland".
Earlier, Margaret McGuckin from the group Survivors and Victims of Institutional Abuse (SAVIA) said the unveiling of the memorial would be a significant moment.
"Where the plaque will be placed, it is in the seat of government," she said.
"When these politicians see it daily, and all these visiting dignitaries from around the world enter into that building, they will see what happened.
"We were failed, children were failed by the state and church."
She said she hopes it will bring a sense of closure for victims.
The Commissioner for the Survivors of Childhood Institutional Abuse, Fiona Ryan, said the memorial was the result of the "courage and conviction" of campaigners.
She added: "If we are pledging to remember, then let us not forget survivors had to fight for the truth to be heard - for the silenced voices of the children they once were to be finally listened to."
The plaque acknowledges that many victims did not live to see justice and accountability.
What was the HIA Inquiry?
The HIA Inquiry examined allegations of abuse in 22 homes and other institutions between 1922 to 1995 and found there was widespread abuse of young residents.
Its final report identified six religious and charitable organisations which, it said, were required to contribute towards the cost of the redress scheme and support services.
So far, payments have been received from the De La Salle Order, the Good Shepherd Sisters and Barnardo's.
The Catholic Diocese of Down and Connor has also made a payment regarding the institutions which it ran with the De La Salle Order.
Stormont officials said they have had "constructive discussions" with the three remaining organisations.
They are the Irish Church Missions, the Sisters of Nazareth, and the Sisters of Saint Louis.
The Executive Office said: "The negotiation process with institutions is continuing and will only be concluded once all redress determinations have been made."
It also said officials would continue to engage with the organisations which have made payments in relation to their final contributions.
Almost 5,500 applications for compensation
The redress board considered the final application for compensation this week.
The total amount of payments is about £116m and there were almost 5,500 applications.
It is understood that the completion of this stage will allow negotiations with the organisations to be finalised.
The amount which each institution has contributed will be published when the process is finished.
What does the memorial plaque say?
The text on the plaque includes: "Between 1922 and 1995, many suffered childhood abuse in residential institutions and were failed by all those who had a duty to protect them, including individuals, organisations and the State.
"Some were sent overseas through the Child Migrant Scheme. These children deserved care, safety, and dignity — but many suffered harm instead."
Concerns had been raised by campaigners when the words "the State" were removed, but it emerged last week that they have been reinstated.
Nine-year delay has 'taken its toll on all of us'
Jon McCourt, from the group Survivors North West, said it had been "a very long road" to get to this point.
"This should not have taken this length of time and it's taken its toll on all of us.
"I have lost my sister and my younger brother since then," he said.
"If it hadn't been for the Assembly collapses we had, and the disagreements, this would have been done within a year."
McCourt added that 2017 "seems so long ago but I remember every word that Anthony Hart said that day".
"This is a tribute to all of those who went through those institutions."
A spokesperson for The Executive Office (TEO) said the plaque will stand as "a permanent acknowledgement" of the children who suffered abuse in residential institutions.
"This has been a phased approach through a public inquiry, specialist support services, redress, a public apology, and a memorial, together representing the Executive's acknowledgement of victims and survivors.
"The event is the culmination of what has been a long, sensitive and detailed engagement process to ensure that the wording on the memorial plaque reflects the views of victims and survivors," they added.