In a statement released yesterday, Thompson described her shame and anger at the allegations, published in The Times on Friday, that Oxfam workers in Haiti had employed beneficiaries as prostitutes in the wake of the 2010 earthquake, and that similar behaviour had happened in Chad.
She said the organisation was ashamed of what had happened and apologised unreservedly.
Thompson, who became a trustee of the charity in March 2017 and was appointed chair the following November, said the charity had made "big improvements" since the allegations were first put to the charity in 2011 but would commit to doing more.
The measures announced today include strengthening the vetting of staff, providing safeguarding training and making safeguarding a mandatory part of the interview process for senior leadership positions.
Oxfam will also establish a new, external whistleblowing helpline to encourage more staff to voice concerns, the statement said.
When news of the allegations broke last week, the Charity Commission said Oxfam had not reported the full nature of the allegations in 2011. As part of the measures announced today, the statement said, Oxfam would "recommit to report to the appropriate authorities in full any issues that arise that could affect the safety of those we work for or the confidence of the public".
Thompson said: "I share the anger and shame that behaviour like that highlighted in Haiti in 2011 happened in our organisation," she said.
"It is clear that such behaviour is completely outside our values and should never be tolerated. Oxfam prides itself on being a transparent organisation that works to make life better for poor and vulnerable people, an organisation that puts women at the heart of everything we do."
The stories in The Times had prompted staff to come forward with concerns about how the members of staff involved in the case had been recruited and vetted, and these concerns would be examined in detail, she said.
She said that she and Mark Goldring, the charity’s chief executive, would be working closely to lead improvements at the charity.
"We will continue to address the underlying cultural issues that allowed this behaviour to happen," she said.
"We also want to satisfy ourselves that we do now have a culture of openness and transparency and that we fully learn the lessons of the events in 2011. Not only will we always be true to those we serve and those who support us, we will also be seen to be so."
She said an ongoing review of the charity’s culture currently being carried out by an independent consultant would be extended to take a detailed look at the case.
"If that review brings about a safer environment for all, then the publicity of the past few days, painful as it has been, will also have been valuable," she said.
Thompson said sexual abuse was "a blight on society" and that NGOs such as Oxfam working in fragile and unstable environments could become targets for abusers.
"We have made significant improvements since 2011 in our efforts to expose and eliminate sexual abuse, but we know we have to be vigilant and to continue to improve if we are to constantly live up to the high standards rightly expected of us," she said.
"It is not sufficient to be appalled by the behaviour of our former staff – we must and will learn from it and use it as a spur to improvement."
The statement confirmed Oxfam would be meeting with Penny Mordaunt, the Secretary of Stat for International Development, who has warned that she could pull government funding from Oxfam because of the scandal.
Speaking on The Andrew Marr Show yesterday, Mordaunt said she believed Oxfam had lied to DfID about the allegations and warned that it did not matter how good safeguarding practices were if an organisation did not have moral leadership.