The official spoke to Eyewitness News on condition of anonymity because the announcement had not yet been made.
The decision opens the door for the Hearst Magazines chairwoman to succeed Schools Chancellor Joel Klein, who is leaving to take a job with News Corp. The 66-year-old Black had needed the waiver because she does not have a background in education.
Mayor Michael Bloomberg had been criticized over his decision to appoint the noneducator to the position, but several high-profile women had endorsed his choice, including Whoopi Goldberg and Gloria Steinem, with whom Black worked at Ms. magazine in the 1970s.
In a letter Friday, Bloomberg said Black would appoint 38-year-old Shael Polakow-Suransky, a former teacher and a member of Klein's administration, to serve as senior deputy chancellor and chief academic officer.
The official told Eyewitness News that Education Commissioner David M. Steiner would grant the waiver Monday.
An advisory panel appointed to weigh Black's qualifications to serve as chancellor had recommended that Steiner deny the waiver that would allow her to serve as chancellor.
Steiner had previously suggested he might be willing to grant a waiver to Black if a second-in-command with academic experience were to be chosen.
Under Black, Polakow-Suransky will be tasked with overseeing the schools' instructional programs and the implementation of major educational policies, the mayor said in his letter to Steiner.
Polakow-Suransky will also advise the chancellor on policy issues relating to curriculum, testing, evaluation and more.
Currently, he serves under Klein as the deputy chancellor for performance and accountability, overseeing school evaluation and capacity building.
A Quinnipiac University Poll showed New Yorkers believed by a 2-1 margin that Black was not qualified for the job. The poll found that 51 percent of city voters believed Black did not have the right experience to serve as schools chancellor.
Just 26 percent said Black did have the experience for the job, and 23 percent were undecided.
Foes and supporters of Black's appointment had been lobbying the mayor since he announced Nov. 8 that he had picked the businesswoman to lead the schools.
New York City Councilman Charles Barron and concerned parent are holding a news conference Saturday morning to voice their opposition and outline possible legal action.
(The Associated Press contributed to this report)