Baraka promised change in a city that was governed for seven years by Cory Booker, elected last year to the U.S. Senate. Baraka first ran for the council in 2010 as a critic of the suburban-raised Booker.
"Today is the day we say goodbye to the bosses," Baraka told cheering supporters Tuesday night.
Baraka will succeed Acting Mayor Luis Quintana on June 30.
Baraka won about 54 percent of the vote Tuesday in the non-partisan race, while Shavar Jeffries, a former New Jersey assistant attorney general and civil rights lawyer, got 46 percent. Two other candidates dropped out before the election.
A native of Newark, Baraka was principal of Central High School from 2006 to 2013, when he took a leave of absence to run for mayor.
In his victory speech, Baraka spoke of his father, who died in January. Amiri Baraka became known in the 1960s under the name Leroi Jones as a poet, playwright and member of the Beats, before becoming a black nationalist and eventually returning to the city of his birth.
"I know his spirit is in this room," Ras Baraka said.
Baraka takes over a city that remains New Jersey's financial center and a cultural hub, but continues to suffer economically after decades of white flight.
Booker attracted national attention because of his unusual background for a Newark mayor as a former Rhodes scholar with an Ivy League education, but critics suggested he was out of touch with much of the city's population.