The previous head of the flagship news and current affairs programme, Peter Rippon, was in charge when an investigation into Jimmy Savile was dropped in late 2011.
Rippon stood aside last October when his explanation in a blog about why the inquiry was pulled was criticised for inaccuracies and had to be corrected.
The job advert for his replacement, published on the BBC's website, reads: "Newsnight is looking for a tough, innovative and creative individual with sound editorial judgment to be the next editor."
Whoever secures the job will be accountable to the head of news programmes, a position also being advertised.
Stephen Mitchell, who resigned from that role in December, was criticised for removing the Savile investigation from a list of the BBC's potentially difficult programmes, known as the "managed risk programmes list".