Around 160,000 children and young people in England provide care for relatives.
The amendment to the Children and Families Bill will mean all young carers under the age of 18 will be entitled to an assessment of their support needs.
Local authorities will also be asked to assess young carers alongside the person they care for, so a “rounded package of support for the whole family” can be provided.
The amendment also simplifies the law relating to young carers, making their rights and duties clearer to both young people and professionals.
Children’s minister Edward Timpson said that although young carers selflessly provide support around the clock for people they love, they can often overlook their own needs.
“This is why we must put in place a system that supports them and enables them to live a full life, as well as protecting them from excessive or inappropriate caring responsibilities,” he said.
“Today’s amendment to the Children and Families Bill will make it easier for these vulnerable young people to get the help they so desperately need, and I know it will be welcomed by many young carers and their families.”
The move represents a victory for children's campaigners, who have long argued for the estimated 160,000 children and young people in England who care for family members to be given the same rights and support as adult carers.
The National Young Carers Coalition (NYCC), a group of charities that campaign on behalf of young carers, said the amendment signalled a “new era of support” for children who care for their parents, siblings and family members.
Moira Fraser, chair of the NYCC and director of policy and research at Carers Trust, said: “The NYCC has been campaigning for over a year for the government to change the law for young carers so that they have stronger rights to assessment and support and protection from inappropriate caring through assessment and support of the whole family.
“We are delighted that the Secretary of State has put forward this proposed amendment and indicated that the Care Bill will also protect young carers.
"Not only will these changes help professionals to understand what they need to do, they have potential to transform the lives of some of our most vulnerable children and young people by helping them and their family when they most need it.”
Matthew Reed, chief executive of The Children’s Society’s, said: “This is an historic moment for children who have the responsibility of looking after their parents, siblings and family members.
"We applaud the government for taking a huge leap to support often incredibly vulnerable young carers who are slipping through the net, undetected by the support services they desperately need."
Barnardo’s deputy director of strategy, Alison Worsley, said the change offers the opportunity to improve the long-term outcomes for young carers.
“We must not forget that despite having some very adult responsibilities, young carers are still children,” she said.
The government announced that it would move to improve the rights of young carers in June this year.