Johnson, who took office last month as the opposition Conservatives' most powerful politician, accused the governing Labour Party of triggering the probe, which he jokingly likened to a "war crime".
The former journalist admitted to having found the red leather cigar case among the bombed-out debris of Aziz's home while visiting Iraq as a reporter in 2003. He wrote about it at the time, and kept it as a trophy of his trip.
Little more was said about it -- until Labour aides unearthed the story during recent campaigning for London mayor, which saw a close-fought race between him and veteran Labour mayor Ken Livingstone.
"They found the article, and with bulging eyes they went to the Metropolitan Police and demanded that I be prosecuted," he wrote in The Daily Telegraph newspaper.
"The poor police have no choice but to investigate this ludicrous affair, and in the interim I am told I must hand the cigar case into police custody -- or else be led in manacles from City Hall.
The 43-year-old jokingly said it was "incredible" that he was being investigated while leaders like US President George W. Bush and former prime minister Tony Blair were not being pursued.
"It seems that a Western politician is finally going to pay the price for his involvement in the Iraq war," he wrote.
But he asked: "Is it Bush or (former US defence secretary Donald) Rumsfeld or (US Vice President Dick) Cheney? Have they found a member of the American administration to take the rap for the disgusting scenes in Abu Ghraib?
"Is it Blair, brought to book after the (House of) Commons failed to impeach him?
"No, my friends, we are not so lucky. None of the major players is going to be arraigned for the Iraq disaster, and the long arm of the law is instead reaching out -- incredibly -- for me."
Defending his actions, he said he even has a letter from Aziz's lawyers stating the former Iraqi foreign minister wishes Johnson to keep the cigar case as a gift.
But, promising to hand the case to police while they pursue their investigation, Johnson underlined the importance of the rule of law.
"It is, after all, what we were fighting for in Iraq," he said.
"It is with a glad heart that I now propose to hand the cigar case over -- though it would be nice, I have to admit, if they arrested Blair and the real culprits instead."