This is according to excerpts of an evening lecture the archbishop is to deliver at Church House, Westminster, in central London, on Monday.
The Nobel laureate is to say Bush and Blair would reap a revival in credibility if they apologise for waging a war that has left the world "a great deal less safe".
"How wonderful if politicians could bring themselves to admit they are only fallible human creatures, and not God, and thus by definition can make mistakes," according to excerpts of the speech published in Monday's Independent newspaper, which is sponsoring the event.
"Unfortunately, they seem to think that such an admission is a sign of weakness," Tutu said. "Weak and insecure people hardly ever say 'sorry'. It is large-hearted and courageous people who are not diminished by saying, 'I made a mistake.' President Bush and Prime Minister Blair would recover considerable credibility and respect if they were able to say, 'Yes, we made a mistake'."
Tutu was awarded the Nobel Peace Prize in 1984 for his non-violent struggle against apartheid in his native South Africa.
In December, Tutu said Saddam should be put on trial before the International Criminal Court in The Hague on the understanding that "he is innocent until proven guilty".
In his speech on Monday, Tutu was to draw a link between Bush's doctrine of pre-emptive attack on rogue regimes and the president's support of capital punishment when he was governor of Texas.
"Weak and insecure people hardly ever say 'sorry'. It is large-hearted and courageous people who are not diminished by saying, 'I made a mistake.' President Bush and Prime Minister Blair would recover considerable credibility and respect if they were able to say, 'Yes, we made a mistake'"
Archbishop Desmond Tutu,
Nobel peace laureate
"It may not be fanciful to see a connection between this and the belligerent militarist policies that have produced a novel and dangerous principle, that of pre-emption on the basis of intelligence reports that in one particular instance have been shown can be dangerously flawed," he was to say.
"And yet were the basis for the United States going to war, dragging a Britain that declared that intelligence reports showed Iraq to have the capacity to launch its weapons of mass destruction in a matter of minutes."
Tutu added that: "an immoral war was thus waged and the world is a great deal a less safe place than before. There are many more who resent the powerful who can throw their weight about so callously and with so much impunity."