The children's rights job is advertised with a salary rang of £90 - £95,000 a year and the closing date for applications is 19 May.
The post is currently held by Keith Towler, whose tenure ends next year.
Wales was the first country in the UK to appoint a commissioner for children in 2001, held by the late Peter Clarke until his death in 2007.
Mr Towler, the second person to hold the job, is unable to reapply for it under the current legislation.
Adverts for the role say that the successful applicant must be able to work effectively with children and young people, to represent their interests at local, national and international levels with a range of organisations.
In February the Welsh government announced plans for an independent review into the role and functions of the children’s commissioner for Wales.
It followed calls from Mr Towler for a review to reflect the developments and changes in Wales since his office was established.
Jeff Cuthbert, the minister for communities and tackling poverty, said, ‘We can be proud that Wales led the way in 2001 when we become the first country in the UK to establish a children’s commissioner, creating a truly independent voice for the needs and concerns of children.
‘I would like thank the current commissioner for his excellent work in the role. The time has now come to begin the process of appointing his successor. We are looking for someone who wants to make a real difference to children and young people’s lives in Wales and ensure they are listened to on issues that affect them.’