Launching the review, Cameron said it will look at which children should be in residential care, and how the system can be improved.
There are currently more than 8,320 children and young people in children’s homes throughout England, making up around 12 per cent of the total number of children in care, with councils spending more than £1bn a year.
“We need to make sure that our residential care homes are doing the best possible job they can," said Cameron, speaking at Prime Minister’s Questions in the House of Commons.
Education Secretary Nicky Morgan, said: “I am crystal clear that only the very best should be acceptable for children and young people in care.
“I want to shine a spotlight on what works, identify barriers to success and end those practices that are holding these children back from a life full of opportunity.
“It is our moral duty to create a care system where all children have access to high-quality care that meets their specific needs. I am confident that Sir Martin’s review will help make this ambition a reality.”
Narey has previously advised the government on its adoption reforms and other children’s issues, including the reform of social work education.
He said: "Some of the best social work I’ve seen has taken place in residential homes, carried out by some outstanding staff.
"And yet there are doubts about whether we use residential care for the right children and frequent disquiet about children’s transitions to adulthood. I am anxious to hear from staff, children, care leavers and those with experience of this sector.”
Cameron has previously indicated that children in care will be a priority over the next five years.
He used his speech at the Conservative Party Conference last month to say that improving outcomes for children in care will form part of an "all-out assault on poverty by government.
And last month Cameron identified children’s services as a “standout area” for reform ahead of the autumn Spending Review.
He said government will adopt a “smarter” approach to public services, running the state more like a business.
The consultation period for the review into children's residential care closes on 31 December 2015 at 5pm. The review is due to report in the spring of 2016.