The combined Lloyds Banking Group later needed a £20 billion taxpayer bailout.
Mr Hornby will appear alongside predecessor Sir James Crosby, HBOS chief executive between 2001 and 2005, at a hearing of the Parliamentary Commission on Banking Standards.
Former HBOS chairman Lord Stevenson will give evidence on Tuesday.
They will be scrutinised on their roles in the bank's pursuit of growth and their attitudes towards the risks it took on.
Mr Hornby is now chief executive of bookmaker Coral and chairman of Pharmacy2U.
Commission chairman, Andrew Tyrie MP, said: "Two of these men were on the bridge when HBOS failed, when public money was needed to rescue it and when trust in our banking system – both within the industry and among the public – collapsed almost completely.
"We will want to know how and why HBOS failed and what lessons can be learned to prevent any future failures from having such a dire impact."