The inquiry and Jeremy Heywood, the country's most senior civil servant, had agreed the "principles that will underpin disclosure" of 25 notes from Blair to Bush and 130 records of conversations between the pair prior to the war.
However, full transcripts and documents will not be published and the material "should not reflect President Bush's views" the head of the inquiry, John Chilcot, wrote in a letter to Heywood.
"Quotes or gists of the content" would be "sufficient to explain our conclusions", he wrote. The inquiry said it had now begun "detailed consideration" of what to release.
The inquiry was set up in 2009 to establish lessons learnt from the war and finished public hearings two years later. However, the publication of its report has been delayed, allegedly because of wrangling over the Bush/Blair papers.
Once the extracts are finalized, those criticized in the report will be given a chance to respond before it is published. It is not clear when that will take place.
NJF/NJF