She is a former executive director of Teach For America, which recruits teachers to work in urban schools.
Anderson has close ties to Newark Mayor Cory Booker. She was an adviser to Booker in his first campaign for mayor in 2002.
The governor's office said Wednesday that Anderson's selection followed a five-month search to identify reform-oriented candidates.
Anderson will head a troubled school district in which nearly half of students do not graduate from high school. The city's schools received a $100 million grant last fall from Facebook founder Mark Zuckerberg.