Lord Saville has begun giving evidence to the Northern Ireland Affairs Committee at Westminster.
His evidence will focus on lessons to be learned from carrying out this type of inquiry in the past in NI and the length and cost of the Saville report.
He will also talk about the adequacy of legislation on public inquiries in the UK.
It is his first time to speak on the inquiry since it was published. He previously turned down two invitations.
The committee members include Northern Ireland MPs Lady Hermon, Naomi Long, Dr Alasdair McDonnell, Ian Paisley and David Simpson.
The Bloody Sunday Inquiry reported on events in Londonderry on 30 January, 1972, when Parachute Regiment soldiers opened fire during a civil rights march killing 13 people.
The report was heavily critical of the Army and found that soldiers fired the first shot.
It concluded that none of the casualties was posing a threat or doing anything that would justify their shooting.
The report was commissioned in 1998 by the then Prime Minister Tony Blair.
The inquiry took more than 2,500 witness statements and became the longest-running and most expensive in British history.
It closed in 2004 with the report initially due for publication the following year. It cost £195m and was to take 12 years in total.