NEW YORK, JAN. 2 -- Minneapolis School Superintendent Richard R. Green was named today as the first black chancellor of the New York City school system, the nation's largest.

Green was the consensus choice of the school board, which will vote formally on Wednesday, board President Robert F. Wagner Jr. said.

Wagner said he had spoken to Green, who said he "was delighted" with the offer. Green cannot formally accept the job until the board approves him in an open meeting, Wagner said.

As chancellor, Green faces the challenge of dramatically improving a school system that is not only the largest, but among the most troubled in the nation.

New York schools are plagued by one of the nation's highest dropout rates, aging and often decrepit buildings and a politically combative hierarchy that makes any change difficult to achieve. The district serves nearly 1 million students in 1,050 schools.

"If public education can work in New York City, it can work anywhere in the country," Green said at a news conference at his south Minneapolis home. "It can work and will. I don't believe in failure."

Green, 51, won out over former deputy chancellor Bernard Gifford, dean of the Graduate School of Education at the University of California at Berkeley. Gifford, who had lobbied heavily for the job, was considered the favorite of the teachers union, while Green was favored by Wagner and Mayor Edward I. Koch (D).

The board reached its decision after last-minute interviews with Gifford and Hernan Lafontaine, the Hartford, Conn., school superintendent.

Green succeeds Nathan Quinones, who was appointed in August 1984 to replace Anthony Alvarado, who had stepped down in the wake of allegations of personal and professional misconduct.

Although Wagner refused to disclose results of the vote by the seven Board of Education members, he said the group met for 45 minutes today at the New York Hilton Hotel before making a decision.