De Quadros studied at the School of Medicine of the Catholic University in Porto Alegre and has a Masters in Public Health from the University of Rio de Janeiro. Since 1969 he has worked with smallpox surveillance in Brazil. That country being free of the disease, he then traveled to Ethiopia, where he was director of field operations for WHO. He then joined PAHO as head of the Area of Immunizations, which led countries to consider immunization programs as a public good.
He also directed the efforts to eradicate polio, of which the last native case in the Americas dates back to 1991, and made possible the eradication of measles and rubella.
In 2001, De Quadros retired from the PAHO and in 2003 joined the Sabin Vaccine Institute, where he is currently vice president.