Labour heavyweight Prescott, who supported the decision in 2003, said he would have to live with the "catastrophic decision" for the rest of his life.
"A day doesn't go by when I don't think of the decision we made to go to war. Of the British troops who gave their lives or suffered injuries for their country. Of the 175,000 civilians who died from the pandora's box we opened by removing Saddam Hussein," Prescott wrote in the 'Sunday Mirror'.
Prescott said Blair's statement that "I am with you, whatever" in a message to US President George W Bush, months before the invasion in March 2003, was "devastating".
Blair, UK prime minister from 1997 to 2007, eventually sent 45,000 British troops into battle without exhausting the peace options, the Chilcot report said.
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"In 2004, the UN secretary general Kofi Annan said that as regime change was the prime aim of the Iraq war, it was illegal. With great sadness and anger, I now believe him to be right," Prescott wrote.
As many as 179 British soldiers and more than 150,000 Iraqi civilians died in the Iraq war in the following years.
The former deputy PM said the Chilcot report had gone into great detail about what went wrong, but he wanted to identify "certain lessons we must learn".
"My first concern was the way Tony Blair ran Cabinet. We were given too little paper documentation to make decisions," he wrote.
Meanwhile, Conservative party MP David Davis said he will file a motion to hold the former PM Blair in contempt of Parliament over Iraq war.
If the motion is accepted, MPs could debate and vote on whether he is guilty of misleading the House of Commons before the summer recess.
"It's a bit like contempt of court. Essentially by deceit," he said.
Referring to the 2003 vote to invade Iraq, he added: "If you look just at the debate alone, on five different grounds the House was misled, three in terms of the weapons of mass destruction, one in terms of the UN votes were going, and one in terms of the threat, the risks.