Education Secretary John Swinney said the proposed new laws would be brought before Holyrood by the end of June to allow for a timetable to be drawn up to bring in the scheme.
It will see the appointment of a single point of contact, such as a teacher or health visitor, to look out for the welfare of all children up to the age of 18 in 2018.
The announcement comes after UK Supreme Court judges ruled elements of the policy were “incompatible” with the right to privacy and family life.
After the legal challenge, Mr Swinney was forced to halt the roll-out of the scheme, which was due to start last August.
The scheme was introduced as part of the the Children and Young People Scotland Act of 2014, with Mr Swinney confirming parts of this would have to be replaced.
Mr Swinney said the new approach would require “named-person service providers and others involved with children and young people to consider whether sharing information would promote, support or safeguard the wellbeing of the child or young person”.
They will also have to consider if sharing information would be compatible with data protection law, human rights and the law of confidentiality. Mr Swinney said: “Only if information can be shared consistently within these legal constraints will there be a power to share it and the legislation will make this clear.”
He added: “This government listened to parents . . . they told us they want the named-person service to work in partnership with them and having a say in the sharing of information about their families matters to them.”
Mr Swinney went on: “The approach seeks to bring consistency, clarity and coherence to the practice of sharing information about children and young people’s wellbeing across Scotland.”
But the Scottish Tories said the scheme had “has run aground” and called for it to be scraped warning that, as it stands, it will “head straight back to the courtroom”.
The party’s education secretary Liz Smith said: “If the SNP had been listening properly it would have recognised months ago it is completely unworkable and unwanted.”
Labour’s Iain Gray called on Mr Swinney to consider excluding 16 and 17-year-olds from the scheme while Lib Dem MSP Tavish Scott said parental concerns still needed to be addressed.
But Martin Crewe, Director of Barnardo’s Scotland said: “The named person policy will mean families know who to turn to for information, advice or assistance, and will ensure that families have access to help as early as possible.”