Mrs Hassan, 59, was abducted in October 2004 and shown later that month on video pleading for her life and calling on Britain to pull its troops from the country. She was killed a month later and her body has never been found.
"An Iraqi man has been jailed for life in a verdict delivered today," the US official who attended the trial said.
The convicted man, Mustafa Mohammed Jubouri, was found guilty of kidnapping Mrs Hassan in October 2004 and shooting her a month later, said another attendee of the hearing, according to AFP.
However a separate report said he was found guilty of aiding and abetting the kidnappers. The other two men were released.
Mrs Hassan had lived in Iraq for 30 years, was married to an Iraqi, and worked for the global humanitarian group CARE International.
One of the highest profile figures to fall victim to the wave of kidnappings sweeping Iraq, she was abducted while on her way to work in Baghdad.
British government blamed
Her family has blamed the British government responsible for her death.
"We believe that the refusal of the British government to open a dialogue with the kidnappers cost the life of our sister," said Deidre, Geraldine, Kathryn and Michael Fitzsimons, in a common official statement.
Deidre Fitzimmons told BBC radio that Britain had treated four phone calls from her captors as hoaxes.
"We were advised by the powers that be that these were hoax calls. But after all they were made on my sister's mobile telephone," she said.
"They were definitely coming from these kidnappers because they would make calls and them they would issue videos and they never made any demands for money," she said.
"My brother-in-law was left in a house on his own without any recording equipment. He was given the advice to say the British didn't want to be involved," Ms Fitzsimmons said.
"After the first call when they demanded to speak to the British, the advice given to my brother-in-law was 'we'll emphasise her Iraqiness' -- which was a ridiculous thing to do after all because they had kidnapped her and taken possession of her British passport.
"The last phone calls were made on November 7. They demanded to negotiate. I don't think he knew what to do. He did the best he could.
"After all this was a man in a house on his own. His wife had been taken hostage. He had seen terrible videos of her and he was really left on his own," Ms Fitzsimmons said. Mrs Hassan was murdered the following day.
The three men on trial in Baghdad were captured by US forces in May last year in possession of Mrs Hassan's personal belongings including her handbag and make-up.