Lord Prescott said he now agreed "with great sadness and anger" with former UN secretary general Kofi Annan that the war was illegal.
He also praised Labour's Jeremy Corbyn for apologising on the party's behalf.
Lord Prescott also said Prime Minister Tony Blair's statement that "I am with you, whatever" in a message to US President George W Bush before the invasion in March 2003, was "devastating".
"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," he went on.
Lord Prescott said he was "pleased Jeremy Corbyn has apologised on behalf of the Labour Party to the relatives of those who died and suffered injury".
He also expressed his own "fullest apology", especially to the families of British personnel who died.