Writing in the UK’s Observer newspaper, he accused the former leaders of lying about weapons of mass destruction.
The Iraq military campaign had made the world more unstable “than any other conflict in history”, he said.
Mr Blair responded by saying “this is the same argument we have had many times with nothing new to say”.
Earlier this week, Archbishop Tutu, a veteran peace campaigner who won the Nobel Peace Prize in 1984 in recognition of his campaign against apartheid, pulled out of a leadership summit in Johannesburg because he refused to share a platform with Mr Blair.
The former Archbishop of Cape Town said the US- and UK-led action launched against Saddam’s regime in 2003 had brought about conditions for the civil war in Syria and a possible Middle East conflict involving Iran.
“The then leaders of the United States [Mr Bush] and Great Britain [Mr Blair] fabricated the grounds to behave like playground bullies and drive us further apart. They have driven us to the edge of a precipice where we now stand – with the spectre of Syria and Iran before us,” he said.
He added: “The question is not whether Saddam Hussein was good or bad or how many of his people he massacred. The point is that Mr Bush and Mr Blair should not have allowed themselves to stoop to his immoral level.”
Archbishop Tutu said the death toll as a result of military action in Iraq since 2003 was grounds for Mr Blair and Mr Bush to be tried in The Hague.
But he said different standards appeared to be applied to Western leaders.
He said: “On these grounds, alone, in a consistent world, those responsible should be treading the same path as some of their African and Asian peers who have been made to answer for their actions in The Hague.” Click on link above to read more.