She pledged support “for many more years to come” after a number of high-profile ambassadors distanced themselves from the charity amid allegations of sexual exploitation.
Ms Eavis, daughter of Glastonbury founder and co-organiser Michael Eavis, said they were “horrified at the reports in the news” but had been assured by the charity they were taking action “to ensure a vigorous safeguarding plan for the future”.
She added: “Let us not forget that abuse of power is a wider issue in society.”
Glastonbury has raised an estimated £6m for Oxfam since launching their partnership with the charity in 1993.
Ms Eavis said she had visited Haiti and met people in remote communities where the organisation is a “lifeline”.
“So we would like to pledge our continued support for Oxfam and the brave and vital work which it undertakes,” she added. “Oxfam do outstanding work all over the world and we firmly believe that the good does still far outweigh the appalling behaviour of the few whose actions have caused such harm.
“We will continue to support Oxfam’s incredible work for many more years to come.”
Nobel Peace Prize winner Desmond Tutu is among those who have quit from ambassador roles at the charity since allegations first surfaced.
The South African emeritus archbishop said he was “deeply disappointed” by the revelations, while actress Minnie Driver and Senegalese musician Baaba Maal also resigned as celebrity ambassadors.
Actor Simon Pegg announced he would stand by the charity as it would be “wrong” to punish the organisation as a whole.
Earlier this week, at the NME Awards, Michael Eavis said: “We’ve raised millions through the years with Oxfam – six million quid and everyone’s said what a wonderful charity they are and we still support them.
“And for a few dodgy people – like with the NHS you get a few dodgy doctors and it doesn’t discredit the NHS does it? So why should it affect Oxfam?”