The Department for Education is imposing a legal duty on councils to provide financial support for those who want to stay longer with foster carers.
The government has pledged Â£40m over the next three years to fund the plan.
A care charity said the measure was the most significant reform for children in care in a generation.
It will be introduced during the third reading of the Children and Families Bill next year.
Children and Families Minister Edward Timpson, whose own family fostered nearly 90 children, said: "I know from the many foster children I grew up with how crucial it is for them to be given sufficient time to prepare for life after care.
Rhiannon was fostered by David and Lisa when she was 16. She is now studying for her A-levels. But as her 18th birthday approached, she was unsure how much longer she would be able to stay.
"The run-up to my 18th birthday wasn't very nice.
"Not knowing what was happening was very stressful and I was crying quite a lot to Dave and Lisa in the evenings about what was going to happen.
"But now I know that they're here for me and it's brilliant."
After discussions with the council, she will now be able to live with the family until she has finished university.
"For me it's important because you know you've got somewhere to stay, somewhere to go back to. You've got the family support that's always there for you."
Her foster parent David says the change will give young people a "better opportunity for the future".
"A growing number of local authorities already offer young people the choice to stay, but with little financial support it can be challenging for their foster families.
"Now all councils will have to follow their example, and we are giving them Â£40m towards the cost.
"This will allow the 10,000 young people leaving stable and secure homes to make the transition from care to independence when they are ready, rather than when their council tells them to."
Speaking to Radio 5 live about the run-up to her 18th birthday Rhiannon Wickham said: "Not knowing what was happening was very stressful and I was crying quite a lot to [my foster parents] in the evenings about what was going to happen.
"But now I know that they're here for me and it's brilliant."
The Who Cares Trust, which campaigns for and supports children in care and young people leaving care, said the move was "absolutely fantastic news for thousands of young people in foster care" and represented "the most significant reform to the support children in care are given in a generation".
Chief executive Natasha Finlayson said: "Time and again we hear from young people who are extremely anxious about having to leave their carers when they turn 18 and effectively no longer having somewhere they can call home, especially when the average age for young people who aren't in care to finally leave home is 24 to 27.
"It is excellent news that the government has agreed that young people leaving foster care should not be left to fend for themselves at 18.
"We mustn't forget though that the 9% of young people in care who live in children's homes - many of whom leave when they are 16 or 17 - need and deserve the same level of support and we hope that the government will start to look towards ways of achieving this."

Andrew Bedford, 27, from Huntingdon, was last seen at 18:20 BST on Friday, 28 September 1990 at Factory Bank, off Great Whyte, Ramsey.
Three people were arrested at the time but no-one was charged.
Specialist equipment is being used to identify disturbances in the earth near Stocking Fen Road in Ramsey.
The investigation into Mr Bedford's disappearance was re-launched as a murder inquiry on Friday.
Police now believe he was shot dead sometime during the evening he was last seen.
Det Sgt Gordon Blair said: "New intelligence has allowed us to pinpoint this area [Stocking Fen Road] as a viable place to search with a view to recovering potential evidence.
"This could include evidence of how Andrew was killed or where his remains are today."
Mr Bedford was last seen eating a takeaway in a light blue Ford Cortina car.
He was wearing overalls, a khaki jumper, jeans and trainers. He was described as 5ft 8in (1.72m), medium build with mousey blond, curly, shoulder-length hair and had a number of tattoos.
The prime suspect for the shooting is now dead, "but others who were involved have never been brought to justice", a police spokesman said.
Children in care in England will be able to stay with their foster families until their 21st birthday, rather than having to leave at 18, ministers say.
[NEXT_CONCEPT]
Officers investigating a cold case murder of a Cambridgeshire man 25 years ago have started digging an area near to where he was last seen alive.