Oxfam's country director in Haiti, Roland van Hauwermeiren, 68, admitted using prostitutes at the villa rented for him by the charity and was allowed a "phased and dignified exit" because a high profile sacking would have "potentially serious implications" for the charity, the report said.
Sources with knowledge of the case said they had concerns about some the prostitutes being underage.
Oxfam has been working in Haiti since 1978. As soon as we became aware of the allegations in Haiti in 2011 we launched an internal investigation. A source quoted by the newspaper said it had seen a video of an orgy with prostitutes wearing Oxfam t-shirts.
In the first wave of humanitarian aid after the natural disaster, Oxfam helped around 700,000 people in the Caribbean country.
The Times reported that the organisation's inquiry was limited by its desire to keep it out of the public's eye.
The report explained that the misconduct related to inappropriate sexual behaviour, bullying, harassment and the intimidation of staff.
It said that it had not been able to prove allegations that underage girls were involved.
According to the British newspaper The Times, Oxfam employees hired young prostitutes in Haiti in 2011 during a mission following the quake that ravaged the country in 2010, killing almost 300,000 people. The charity had a 70 million pound fund - more than NZ$133 million - for relief supplies and to help rebuild the country's infrastructure, the Times reported. Still, none of the accused staffers have been arrested or faced criminal charges.
But a small group of male aid workers living in Delmas, near Port-au-Prince had turned the guesthouse Oxfam had rented for them into what a source told the Times the men called "the w.house". "It was unbelievable. It was insane", the source told the Times, about parties at the house.
In October previous year, the Times also reported seven senior officials at the charity have been investigated for misconduct including sexual harassment.
The Charity Commission told the Times it did not get the final investigation report and it had asked Oxfam to "provide us with assurance that it has learnt lessons from past incidents and is taking all necessary steps to ensure risks are minimised".
The UK's Department for International Development (DFID) said Oxfam's leaders "showed a lack of judgment" in the way they investigated the case and in communicating with the government and the British commission that control humanitarian organizations.
The Times reported on Friday that the government secretary responsible for charity regulation was calling for Oxfam to provide more information about the charity staff who had paid for sex in Haiti.
President of Murray Edwards Dame Barbara Stocking is facing allegations that she was involved in the cover up of a recent Oxfam scandal, in which prostitutes were hired by aid workers in Haiti.