Aileen Campbell said the move - which is expected to be approved by Holyrood today - was a "significant change" to the system.
Young people can currently remain in care until they are 19, but many leave earlier at the age of 16 or 17.
But from April next year, teenagers in residential, foster or kinship care will have the right to continue to receive this care until the age of 21, with the Scottish Government providing £5 million a year, up to 2020, to fund it.
The reform is included in the Children and Young People (Scotland) Bill.
Ms Campbell said: "It has been clear to me since we set out to transform family services that we must ensure all young people in care have access to a range of excellent care and support that they know they can rely on as they head into early adulthood.
"We have committed £5m every year up to the end of this decade."