Sir John said national security vetting of the report had been completed and it would be published without any material being redacted.
Relatives of the 179 British service personnel killed in Iraq between 2003 and 2009 will get “early sight” of the 2.6 million word report, he added.
The inquiry was launched in 2009 into the UK’s participation in the US-led invasion of Iraq and its aftermath – which saw British troops remain on Iraqi soil for six years.
Prime Minister Cameron told the inquiry head last November he was “disappointed” at the time it was taking to release the findings and urged him to “expedite” the final stages. Its publication will come 1,981 days after the inquiry ended.
Conservative former front-bencher David Davis last month claimed lives had “probably” been lost as a result of the delays because Britain had made recent interventions in Libya, Syria and Iraq without proper knowledge of the controversial 2003 choice to go to war.
Publication was delayed by a process under which those who may face criticism are given the opportunity to respond before publication.
Tony Blair denied last year that he was responsible for the hold-ups. Critics have long suspected the former prime minister of wanting to spin out the investigation in which he is expected to be criticised and he has faced accusations that he sought to block publication of his communications with US president George Bush.
In May 2014, Sir John disclosed he had finally reached agreement with the Cabinet Secretary Sir Jeremy Heywood on the disclosure of Mr Blair’s discussions with Mr Bush, three years after Sir Jeremy’s predecessor, Sir Gus (now Lord) O’Donnell, ruled they could not be released in their entirety.
More than 150 witnesses gave evidence to the inquiry.
It has analysed more than 150,000 government documents as well as other material related to the invasion.
Last summer, families of soldiers killed in the Iraq War threatened legal action over the delays. Rose Gentle, whose Royal Highland Fusilier son Gordon, 19, of Glasgow, was killed in a bomb attack in Basra in 2004, said she was “glad” the date had now been announced. She said: “We just hope everything we want to be in it is actually in it.”