The appointment reflects de Blasio's desire to make sweeping changes to the educational policies of outgoing Mayor Michael Bloomberg, the New York Times reported.
"We cannot continue to be a city where educational opportunity is predetermined by ZIP code," de Blasio said in describing how he expected Farina to help all children realize their potential.
Farina, 70, is a veteran of New York City schools, working as a teacher, principal and district superintendent in a career that spanned four decades. She retired as a deputy chancellor in 2006 over concerns about the growing use of standardized tests to evaluate students.
De Blasio said he would reduce the emphasis on such tests.
"We're going to have a system here where parents are seen as real partners," Farina said after her introduction in the chilly gymnasium of a Brooklyn middle school attended by both of de Blasio's children. "And teachers are going to understand that working with parents enhances their work in the classroom."
Since retiring, Farina had become a vocal critic of Bloomberg's education policies. During a speech in November, she said she wanted a school system "where people do things because they have a sense of joy about it, not because they have a sense of fear."