But Professor John Catford, 45, chief executive of Health Promotion Wales, strongly denied an MP's allegation that he had fiddled his expenses.
Professor Catford appeared at a Cardiff hotel with his wife Lucinda and read a statement admitting his affair, but insisted there had been no abuse of taxpayers' money.
Earlier, in a Commons motion, Labour's health spokesman on Wales, Rhodri Morgan, MP for Cardiff West, called on John Redwood, Secretary of State for Wales, to set up an inquiry into the authority's administration, claiming that Professor Catford had charged expenses for attending a conference in Brazil that never took place.
Professor Catford, a father of four, resigned within two hours. His statement said: 'In August 1991 I went on a professional trip to Brazil to study public health in a developing country.
'The eight-day trip was taken during my annual leave . . . To my deep regret, I became involved in a relationship with a female colleague. After Brazil, I saw her once more in Rome in November 1991 and our relationship was ended then.
'The brief affair was silly and regrettable. However, the visit was entirely above board and legitimate. There was no abuse of public money.'
Professor Catford, who is paid a combined pounds 80,000 salary from the authority and the University of Wales Medical School, has been on sick leave since December.
Last night he said the theft of photos and a diary from a locked filing cabinet in his office had led to a health authority investigation into overseas travel.
'They were personal papers about the relationship, photos and a short diary of our feelings for each other. I don't know what happened to these papers, but I believe they were made available to my employer.'