The colourful former editor was behind a number of controversial front-page Sun headlines, including "Freddie Starr Ate My Hamster" and "Gotcha" about the sinking of the Argentine warship General Belgrano during the Falklands War in May 1982.
Now a columnist for the Daily Mail, he is expected to be asked about the process of checking the facts of a story.
In his speech in October, he said: "My view was that if it sounded right it was probably right and therefore we should lob it in."
The current editor of the Sun, Dominic Mohan, will also give evidence to the inquiry into press ethics today.
The former showbusiness reporter became editor in 2009 and will be the first of seven current national newspaper editors to appear.
Lord Justice Leveson will also hear from the Sun's royal editor Duncan Larcombe, showbusiness editor Gordon Smart and legal manager Justin Walford.
Former editors Stuart Higgins and David Yelland will give evidence via witness statements.
Prime Minister David Cameron set up the Leveson Inquiry last July in response to revelations that the News of the World commissioned a private detective to hack murdered schoolgirl Milly Dowler's phone after she disappeared in 2002.
The first part of the inquiry, sitting at the Royal Courts of Justice in London, is looking at the culture, practices and ethics of the press in general and is due to produce a report by September.
It began taking evidence in November, and has heard a series of complaints about media intrusion from celebrities and the families of murdered and abducted children.
The inquiry's second part, examining the extent of unlawful activities by journalists, will not begin until detectives have completed their investigation into alleged phone hacking and corrupt payments to police, and any prosecutions have been concluded