The new chair is expected to take over at the beginning of the new year, after the departure of Lord Grade, who is due to step down at the end of December, having chaired the regulator since its inception three years ago.
The advert says the job will be based in London and will involve a time commitment of one day a month, with remuneration of £500 a day.
It is essential for the successful applicant to be "an acknowledged leader" with previous experience of sitting on a public, private or charitable board, "substantial knowledge and experience of the charitable sector" and "knowledge and experience of regulation", the advert says.
Candidates must also have "an understanding of devolution and its implications in the nations of the UK" and experience of dealing with the media "in challenging environments", the advert says.
"Professional knowledge of charitable fundraising" is listed as desirable.
The deadline for applications is 10 September, with interviews taking place on 31 October.