It was called for as part of a settlement of a lawsuit involving former residents of the two institutions.
The settlement for $32.7 million was reached in December and approved by a judge in February.
The class actions were launched by former residents of the Rideau Regional Centre in Smiths Falls, Ont., and the Regional Centre near Chatham, Ont.
Court heard many suffered physical and sexual abuse at the overcrowded and understaffed prison-like institutions.
Rideau opened in 1951 and Southwestern in 1961 but both were shut down about a decade ago.
"If Ontario is to have a brighter, stronger future, we must — as a government and as a society — take responsibility for the wrongs of the past," Wynne said in a statement.
"Families of the residents of the Rideau and Southwestern Regional Centres trusted the government to care for their children, grandchildren, brothers and sisters. In too many cases, the government failed to uphold this trust."