He will take the role of independent chair with a focus on ensuring there are enough adopters in the system for children waiting to be adopted.
The government announced the creation of the board at the end of last year as it looks to speed up and improve the adoption process.
Narey said: “There is still much more to be done before every child in England who needs the love and permanence that adoption brings finds an adoptive home speedily.
"And there is a great deal more needed to ensure that adoptive parents receive all the support that is necessary to ensure that their adoption succeeds."
As well as monitoring progress of adoption reform, the board will advise ministers on adoption policy.
It includes representatives from councils and voluntary adoption agencies, such as chief executive of the British Association for Adoption and Fostering Srabani Sen
and David Simmonds, chair of the Local Government Association’s children and young people board.
Children’s minister Edward Timpson added: “We know there is still a shortage of adopters and that work needs to be done to ensure the 6,000 children who need a safe and caring home are placed more quickly.
“That is why our new Adoption Leadership Board will play an important role in ensuring that not only local authorities and adoption agencies stay on track but that we do what we can to improve the system and recruit even more adopters than ever before.”
Latest Department for Education research estimates there could be potentially four million people in England who would consider adopting. There are around 6,000 children waiting to be adopted.
Among government reforms is the establishment of a £19m Adoption Support Fund for adoptive families in areas such as early years support and priority in school admissions.
Also created is the First4Adoption information service, which aims to link prospective adopters with agencies.
According to latest figures for its first year in operation the service attracted 2,000 calls and saw 95,000 visits, of which more than 6,800 went on to directly contact an adoption agency.