The appointment puts Ms. Fariña, 70, in charge of the nation's largest school system at a time of sweeping reforms, though with a mandate to rethink many of the Bloomberg administration's educational policies of the last 12 years.

"We cannot continue to be a city where educational opportunity is predetermined by ZIP code," Mr. de Blasio said, describing how Ms. Fariña as chancellor will help all children realize their potential.

He said Ms. Fariña was a "brilliant innovator" and a leader and educator who is "universally recognized" and would garner immediate respect from teachers, principals, parents and others.

The mayor-elect made his announcement in the chilly gymnasium of Middle School 51, in Brooklyn's Park Slope neighborhood, which is closed until early next month for winter break. Still, a group of more than 30 children were positioned behind the speakers for the announcement. Ms. Fariña will succeed Dennis M. Walcott.

Some parents of the children, and some teachers, stood off to the side, many smiling, in a school Mr. De Blasio said was dear to his family because his son and daughter graduated from there.

Mr. de Blasio acknowledged the way much of the current policies on testing, school closings and charters is tied to federal and state regulations and policies.

"I know that the challenges ahead are just obstacles to be met," Ms. Fariña said.

Ms. Fariña drew heavily on her life's experience to describe how meaningful education has been to her. She said her grandchildren cheered her on in considering the post, calling her the greatest teacher in the world, she said. Her father inspired her, she said.

Ms. Fariña, dressed in a black and red pantsuit, stood next to Ursulina Ramirez, who will be her chief of staff.

The choice reflected Mr. de Blasio's desire to depart radically from the educational policies of Mayor Michael R. Bloomberg, including the emphasis on data and policy of shuttering low-performing schools. The choice is also in keeping with Mr. de Blasio's pattern of appointing people with deep governmental experience.

Ms. Fariña, the daughter of immigrants from Spain who fled the Franco regime, is a veteran of the city's school system, having served as a teacher, principal and superintendent of a Brooklyn school district.

She has stood out throughout her career with her blunt style and egalitarian ideals, first becoming known within the system as a principal at Public School 6 on the Upper East Side of Manhattan. In 2004, she was named a deputy chancellor in the Bloomberg administration, but retired two years later, uneasy about the growing use of student test scores to evaluate schools.

As the leader of the nation's largest school district, with 1 million students, Ms. Fariña will face a host of thorny issues, including calming tensions over a new set of academic standards, rolling out a plan to charge rent to charter schools and negotiating a contract with the city's teachers' union, which is demanding billions of dollars in retroactive raises.

Mr. de Blasio has spoken often about his desire to break with several hallmarks of the Bloomberg era, including its support of charter schools. He has said he will decrease the emphasis on standardized testing and give more input to parents.

Ms. Fariña shares Mr. de Blasio's skepticism of standardized testing and his focus on early education. As chancellor, she will help shape his proposal to expand access to preschool and after-school programs.

The search for a chancellor stretched on for almost two months. It is considered one of Mr. de Blasio's most important appointments, given the emphasis he placed on education during his mayoral bid, including his signature proposal for universal prekindergarten.

But the process of picking a chancellor apparently was not easy. Several candidates withdrew from consideration, including Kaya Henderson, chancellor of the schools in Washington, D.C. Other high-profile contenders included Joshua P. Starr, who leads Montgomery County Public Schools in Maryland, and Kathleen M. Cashin, a longtime city educator and member of the Board of Regents.