She will take up her post May 1, replacing retiring UNICEF Executive Director Carol Bellamy, another American, who served 10 years in the post.
"I'm sure you can imagine, she is not an easy person to replace," Annan told reporters at U.N. World Headquarters in New York, saying Bellamy served UNICEF "with exemplary skill, determination and conviction, facing numerous challenges along the way."
Annan said Veneman's "qualifications are outstanding."
"She has focused strongly on new ways of feeding the hungry around the world -- thus making an important contribution to the first of the eight Millennium Development Goals," he said. "And she has been a long-term and steadfast supporter of programs to advance the welfare of children, both at home and abroad."