"This is a long-called-for step recognising the bond between healing, dignity and the health and wellbeing of members of the Stolen Generations, their families and their communities," Morrison told Parliament.
"To say formally not just that we're deeply sorry for what happened, but that we will take responsibility for it," Morrison added.
Pat Turner, the Northern Territory-based Indigenous chief executive officer of the National Aboriginal Community-Controlled Health Organisation, welcomed the compensation, which was recommended in 1997 by a government inquiry into the Stolen Generations.
"Many of our people have passed, including my mother, so it's a sad day for those who have passed, but it's a good day for those who have survived," Turner told Australian Broadcasting Corp.
Turner's mother Emma Turner had been taken from her own mother in the 1920s and they didn't reunite until the 1970s.
"It will never replace growing up with family, you can never replace that," she added. "I hope this will give some relief to the survivors of the Stolen Generations."
Indigenous Australians account for 3 per cent of the population and have poorer health, lower education levels and shorter life expectancies than other ethnic groups. Indigenous adults account for 2 per cent of the Australian population and 27 per cent of the prison population.
A centre-left Labor Party government launched the ambitious Closing the Gap initiative in 2008 aimed at achieving equality for Indigenous Australians in health and life expectancy within a generation.
But Morrison's conservative government last year scrapped the 12-year-old timetable, declaring the policy had failed.
Morrison said that among the most significant achievements of Australia's pandemic response were the facts that Covid-19 had been kept out of Outback Indigenous communities and no Indigenous Australian had died from coronavirus.
-AP