Mr Blair's book, A Journey, reveals the extent of the rift between two men who dominated British politics from the moment New Labour stormed to power in 1997 to its capitulation at the polls in May.
The former PM says he was put under "relentless personal pressure" by Mr Brown but could not sack his Chancellor because he feared it would lead to him being ousted from No. 10.
He writes: "It is easy to say now, in the light of his tenure as Prime Minister, that I should have stopped it; at the time that would have been well-nigh impossible."
The words that Tony Blair uses are pretty powerful and... if there are old wounds to be reopened then they might just do it.
Sky News' deputy political editor Joey Jones
Mr Blair says one of Mr Brown's great weaknesses was that he lacked political instincts.
"Political calculation, yes. Political feelings, no. Analytical intelligence, absolutely. Emotional intelligence, zero."
But Mr Blair also acknowledges the strengths that made Mr Brown such a formidable rival.
"Was he difficult, at times maddening? Yes. But he was also strong, capable and brilliant, and those were qualities for which I never lost respect."
Gordon Brown stands down as PM after losing the general election in May
At one point in his book Mr Blair says he concluded that unless Mr Brown defined himself along New Labour lines his premiership "was going to be a disaster. I knew it".
On Iraq, Mr Blair says he was "desperately sorry" for the relatives of those killed in the conflict.
But he insists leaving Saddam Hussein in power would have been a "bigger risk" to security than removing him.
Mr Blair meets British troops in Iraq in 2005, two years after the US-led invasion
The former Labour leader says he was angry at the way he was questioned at the Chilcot Inquiry when asked if he had any regrets about the decision to go to war.
He writes the inquiry "had inevitably turned into a trial of judgement and even good faith" rather than being about learning the lessons of the conflict.
In the book, Mr Blair also hints that Mr Brown ratcheted up pressure over the cash-for-honours scandal in a clash over pensions reform.
Mr Blair gives evidence at Sir John Chilcot's inquiry into the Iraq war
Sky News' deputy political editor Joey Jones said: "The words that Tony Blair uses are pretty powerful and... they are the sort of things that if there are old wounds to be reopened then they might just do it."
Jones added that Mr Blair's comments on his Chancellor "and his rather casual dismissal of Brown's premiership, is the sort of thing that will enrage Mr Brown".
The book covers events from throughout Mr Blair's political life, from his election as Labour leader in 1994 to the death of Diana, Princess of Wales, the Northern Ireland peace talks, war in Bosnia, Kosovo and Afghanistan, and the struggle against terrorism.
What we get is the man we know: self–deprecating but steely, willing to admit tactical mistakes but unbending that his strategic vision was right.
Adam Boulton, Boulton & Co.
In it, Mr Blair also reveals he used alcohol as a "prop", although he says he never became a "toper". He would drink a whisky or gin and tonic before his evening meal, then have several glasses of wine.
"So not excessively excessive. I had a limit. But I was aware that it had become a prop," he writes.
Mr Blair is donating all profits from the book, denounced by anti-war protestors as "the memoirs of a war criminal", to the Royal British Legion to help fund a new sports centre for injured troops.
