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."
The same legislation will also increase free childcare for three and four-year-olds so these youngsters, as well as vulnerable two-year-olds, can get 600 hours of funded care a year from August.
Meanwhile, Scottish Government plans could see youngsters benefit from 1140 hours of free childcare a year if the SNP is voted into power in an independent Scotland.