Applications will open on Tuesday although the planned public event will no longer take place.
Jon McCourt of the Survivors North West Victims group said it was a positive move.
Victims have already endured long delays in their campaign for recognition and compensation.
Paying compensation to those who suffered harm when they were in homes run by the church and state was among recommendations from the Historical Institutional Abuse (HIA) public inquiry in 2016.
It examined allegations of physical, emotional and sexual harm of children in residential institutions between 1922 and 1995.
But the collapse of Stormont in January 2017 delayed that process.
In December, the head of the Northern Ireland Civil Service, David Sterling, said the application for abuse payments for those victims and survivors of historical abuse would open in March.
Mr McCourt had expressed concern the opening of the process could be delayed due to the ongoing coronavirus lockdown, while understanding the difficulties it posed.
He welcomed the development that the launch of the redress process will happen as planned on Tuesday.
However, the pandemic will still have an impact on other steps planned.
It is understood that applications will initially be made online through a solicitor’s office, while face-to-face meetings may not be able to take place initially due to social distancing rules.
The Headline Building, which is the office of the Redress Board headed up by Mr Justice Colton, is currently closed as a safeguard against Covid-19.
The record storage facility at the Public Records Office for the North of Ireland (PRONI) is operating with limited capacity.
Mr McCourt said access to the records is essential for verification purposes for applicants who gave evidence to the HIA inquiry.
“This will all add to the length of time it will take to make and process applications,” he told the Press Association news agency.
“But 10 years and four months after bringing the issue of Historical Institutional Abuse to the Assembly chamber, and three years and two months after the Historical Institutional Abuse Inquiry report was released, we are finally seeing the launch of the Redress Process.
“We do not underestimate the uncertainty that there has been over the start of the redress process.
“It has been a long time getting to this point.”
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