The 84-year-old Leoz, who had heart surgery for the fourth time in December, has headed CONMEBOL since 1986, and been on FIFA's executive committee since 1998.
"I have invited you to this meeting to share with you my retirement from FIFA," Leoz told Reuters, before adding that he had informed president Sepp Blatter of the news.
"I'm announcing my retirement from all FIFA commitees because it's important for my life," the Paraguayan continued. "I still have good mental health but physically I'm often impeded. I feel very happy, because I'm retiring with the tranquility and knowledge of having done a sincere and honest job."
In 2010 Leoz was accused by the BBC program Panorama of having received money from ISL, a former marketing partner of FIFA. He denied any wrongdoing. The findings of a FIFA investigation into accusations of bribery involving ISL had been due in March but could now be put forward as early as this week.