The Children's Wellbeing and Schools Bill will also make sure that teachers and schools are always involved in decisions around safeguarding children in their area, and that if a child's home environment is assessed as unsuitable or unsafe, local authorities have the power to intervene.
A unique identifier number will be given to children across services, similar to an adult's national insurance number.
Under the government's plans, parents will no longer have an automatic right to educate their children at home if their child is under a child protection plan, and will have to acquire the local council's permission first.
The previous government had also proposed creating a register of children who are not in school.
But the Children's Charities Coalition, representing Action for Children, Barnardo's, the National Children's Bureau, the National Society for the Prevention of Cruelty to Children (NSPCC), and The Children's Society, said: "The money announced today falls far short of what's needed.
"Children and families desperately need - and deserve - sustained investment in early help services, mental-health support and children's social care.
"This needs to be underpinned by an ambitious strategy to tackle child poverty."
The Education Policy Institute warned that up to 300,000 children may be missing from education entirely.
Children's Commissioner Dame Rachel de Souza said she had "called on successive governments to introduce a unique identifying number for children and a register of all children not in school".
"Writing these two landmark measures into law will be of huge significance for any child currently at risk of harm in this country.
"It must now be supported by proper data-sharing between organisations so no child can become invisible in the system."
The general secretary at the school leaders' union NAHT, Paul Whiteman, also welcomed the bill, saying they had "long called for a register of pupils who are not in school" and "it is very positive to see that this important safeguarding measure is finally being taken, after years of delay".
The register is expected to come into force in 2025.
First unveiled in the King's Speech, the Children's Wellbeing and Schools Bill is wide-ranging in its proposals, including free breakfast clubs in all primary schools and legislation to limit branded uniform items.