The Scottish Government announced that from April next year teenagers in either residential care, foster care or kinship care will have the right to continue to receive this care until the age of 21.
The Government will also provide funding of £5 million a year, up to 2020, for this.
While young people can currently remain in care up until the age of 19, the charity Who Cares? Scotland said in practice many leave care at the age of 16 or 17.
A spokesman for the Scottish Children's Services Coalition (SCSC) - which includes Who Cares? Scotland and other children's service providers from the voluntary and independent sectors - said the change would mean Scotland would be a "world leader when it comes to addressing the challenges faced by many young care leavers."
The Scottish Government plans to amend the Children and Young People Bill, which is currently going through Holyrood so that all young people in care born after April 1999, will have the right to stay in foster, kinship or residential care until they reach the age of 21.
Ministers also propose to extend the right to aftercare support for those who have been in care, so that this will be available up until the age of 26, instead of 21.
The long-term ambition of the Scottish Government is to give young care leavers up to the age of 21 the chance to go back into care, if they feel they need this support.
Children's minister Aileen Campbell announced the changes, saying: "It is vitally important that the support available to young people leaving care will help make the transition to independent living as comfortable and successful as possible.
"Care leavers in Scotland currently receive care and financial support up to the age of 21 and we have already committed to extending this to 26.
"We are now able to announce that, from April next year, those 16-year-olds in foster, kinship or residential care will have a right to stay up until the age of 21 before receiving aftercare.
"We are committing £5 million a year for these improvements as we take steps with our partners in the sector to give young people in care the same opportunities and positive future that their non-looked after peers enjoy."
She said the proposals came following "extensive work" with key groups like Barnardo's, Aberlour, Who Cares? Scotland and local councils, and would "help hundreds of vulnerable young people achieve their full potential".
The changes have already been welcomed by those working with young people in care.
The SCSC spokesman said: "This move by the Scottish Government after significant lobbying, including by young care leavers themselves, is to be greatly welcomed.
"It will prove a life saver, literally, for many young people in care who together represent some of the most marginalised young people in our society and demonstrates that Scotland truly is a world leader when it comes to addressing the challenges faced by many young care leavers."
Duncan Dunlop, chief executive of Who Cares? Scotland, said: "The number of young care leavers who will benefit from these changes is significant and I don't know of any other country in the world who has made a commitment like this."
He hailed the reforms as a "significant change for Scotland's most vulnerable and stigmatised young people".
Jackie Hothersall, director of children and families services at the Aberlour Child Care Trust, said the changes would "strengthen the way we support looked-after young people".
She added: "By increasing the age of leaving care in Scotland to 21 and by increasing the support that those young people receive when they leave care, we can help secure a more positive future for Scotland's young people.
"This policy will allow young people who are in care the kind of support that those in the family home rely on as they begin to find their feet in the world.
"There are 15,000 looked-after children in Scotland at any given time and their life chances will be unquestionably be improved by these changes."
Martin Crewe, director of Barnardo's Scotland, said: "Allowing care leavers to return to some form of care, and increasing the number who can receive enhanced support after leaving care, will help particularly vulnerable young people when they need it the most."
Carol Iddon, director of children's services (UK North) at Action for Children, said: "The trauma that many children experience before being taken into care can mean that they are not ready to leave home as teenagers - many are forced to live independently at just 16 years old and we know it can be a dangerous and lonely experience. That is why today's announcement is a vital step forward.
"It is great to see the Scottish Government taking a lead in committing to provide young people in all forms of care, not just foster care, with the support they need and deserve.
"We look forward to brighter futures for this generation of looked-after children and those to come."
Opposition politicians at Holyrood also welcomed the proposals.
Labour education spokeswoman Kezia Dugdale said: "I am delighted for care leavers and the organisations working to support them that the Scottish Government has now listened to what they, along with Labour MSPs, have been saying on the need for improved access to services for looked-after children as they reach adulthood.
"For any child leaving home it is a process that requires support and it's only right that this is made available to those leaving care as well, which is why I called for a ten-year plan to improve the standard of support available to care leavers. Aileen Campbell has now agreed to go forward with this plan which is the right thing to do.
"Providing the option to return to care up to the age of 21 will give these vulnerable youngsters access to a more secure background from which they can reach their full potential and give them the sense of security that those of us lucky enough to have the stability of family often take for granted."
Liberal Democrat education spokesman Liam McArthur said: "This is a welcome change of heart from the Scottish Government.
"While these proposals were not initially supported by ministers, I am pleased that they have relented following pressure from the Education Committee and charities involved in supporting those going through the care system."
He urged the Government to look again at using the Bill to extend childcare for two-year-olds from the poorest families, saying: "If this approach is good enough for care leavers, surely it is good enough for our most disadvantaged two-year-olds."
Councillor Douglas Chapman, the spokesman for education, children and young people for the local government body Cosla, gave his backing to the reforms, saying: "The announcement today by Scottish Government on throughcare and aftercare is welcomed by local government.
"Good quality throughcare and aftercare is crucial at determining the future prospects of former looked-after children, and this is recognised by local authorities who already go beyond what is required of them by law. Cosla has been working closely with government and the voluntary sector on the extension of support proposals."
Mr Chapman added: "We recognise that the changes proposed by the Government will have additional financial implications for local authorities which will have to be met, but we have an agreement with government that all provisions within the Children and Young People Bill will be fully funded.
"With government, we will be monitoring the implementation of the legislation to ensure that local authorities have sufficient resource to meet the ambitions of the Bill.
"This is a positive announcement to start 2014 and we look forward to working with government and our partners in the children's voluntary sector to ensure we continue to deliver for Scotland's most vulnerable children and young people."