In a letter to the Prime Minister Sir John said that the two million word report would be ready for publication in June or July 2016, seven years after the inquiry was set up by Gordon Brown.
It comes after growing pressure from David Cameron and other campaigners and senior politicians to speed up the timetable of publication.
When Mr Brown commissioned the report he said it would take “at least a year”.
In the end the inquiry heard 130 sessions of witness evidence and received 150,000 documents.
In the letter, delivered to Mr Cameron as he travelled to Iceland, Sir John said that he intended to complete the text of the report by the 18th April. From that point until June or July the contents would be checked by National Security officials.
Sir John wrote: “National Security checking is distinct from the process of declassifying material for disclosure in the Inquiry’s report. Its purpose is to ensure that the Government’s obligations under Article 3 of the ECHR and for the protection of National Security will not inadvertently be breached by publication of the Inquiry’s report as a whole.
“The Inquiry will obviously seek to ensure no such breach might occur, but I entirely understand that a checking process is necessary and is normal procedure in Inquiries which have considered a large volume of sensitive material, as we have.”
The Prime Minister will respond to the letter later today.
Last week Tony Blair apologised for “mistakes” in the planning of the Iraq war.
In an interview with CNN he said: “”I apologise for the fact that the intelligence we received was wrong.”
“I also apologise for some of the mistakes in planning and, certainly, our mistake in our understanding of what would happen once you removed the regime.”