From private talks between George Bush and UK PM Tony Blair, the memo makes it clear the US was determined to go to war whether or not he had UN backing.
He is quoted discussing ways to provoke Saddam Hussein into a confrontation.
A UK lawyer quoted the note in a book published in January but this is the first time it has been seen in full.
White House spokesman Scott McClellan refused to discuss the contents of the memo but said that up until the last moment, President Bush was interested in pursuing a diplomatic solution to the Iraq issue.
The five-page memo, dated 31 January 2003, was written by Mr Blair's then chief foreign adviser, David Manning, the New York Times says.
Summarising the two-hour White House meeting, the memo says: "Our diplomatic strategy had to be arranged around the military planning."
Mr Bush is paraphrased as saying: "The start date for the military campaign was now pencilled in for 10 March. This was when the bombing would begin."
Although the US and UK pushed for a second UN resolution on Iraq, the memo cites Mr Bush saying he did not believe one was needed.
"The US would put its full weight behind efforts to get another resolution and would twist arms and even threaten," Mr Bush is paraphrased as saying.
"But he had to say that if we ultimately failed, military action would follow anyway."
Mr Blair is described as responding that both countries must make clear the second resolution was "Saddam's final opportunity".
According to the note, he also told Mr Bush: "If anything went wrong with the military campaign, or if Saddam increased the stakes by burning the oil wells, killing children or fomenting internal divisions within Iraq, a second resolution would give us international cover, especially with the Arabs."
The UK government has always insisted military action was used as a last resort against Saddam Hussein's regime.
Downing Street has stressed Mr Blair only committed UK forces to Iraq after securing the approval of the House of Commons on 18 March 2003.