As the U.S. District Court for the Northern District of Mississippi put it, Cleveland — a town of 12,000 — has been running an illegal dual system for its black and white children, failing year after year to reach the “greatest degree of desegregation possible.”

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Now Cleveland must consolidate its schools, integrating all its students into one middle school and one high school.

The order, written by Judge Debra M. Brown and released late Friday, comes 62 years after the U.S. Supreme Court issued its landmark ruling on school desegregation in Brown v. Board of Education. And it comes a half-century after Cleveland families first sued the district for continuing to operate racially segregated schools.

“The delay in desegregation has deprived generations of students of the constitutionally-guaranteed right of an integrated education,” Brown wrote. “Although no court order can right these wrongs, it is the duty of the district to ensure that not one more student suffers under this burden.”

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District officials had argued that the Justice Department’s consolidation plan would trigger white flight, making it all the more difficult to achieve integration. They had put forth two alternative plans that would have kept the two high schools open, relying on choice and magnet programs to try to create diversity.

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The court found both of those plans unconstitutional. The district had already tried to use choice as an engine for integration, and it hadn’t worked at the secondary level.

“This decision serves as a reminder to districts that delaying desegregation obligations is both unacceptable and unconstitutional,” said Principal Deputy Assistant Attorney General Vanita Gupta, head of the Justice Department’s Civil Rights Division, in a statement. “The court’s ruling will result in the immediate and effective desegregation of the district’s middle school and high school program for the first time in the district’s more than century-long history.”

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Cleveland Superintendent Jacquelyn C. Thigpen did not immediately respond to a request for comment.

Federal officials estimate that the district’s new consolidated middle school will enroll 692 students, 71 percent of whom will be black and 26 percent of whom will be white. In 2015, Cleveland’s D.M. Smith Middle School had 248 students, 99.6 of whom were African American. Margaret Green Middle School enrolled more than twice as many students; 51 percent of them were African American and 43 percent were white.

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The consolidated high school will enroll an estimated 1,098 students: 63 percent black and 32 percent white. Currently, one high school is 100 percent black and the other is 45 percent white and 47 percent black.

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The Rev. Edward Duvall, an African American parent of two children in the district’s public schools, said he favored consolidation in part because it would save money, leaving more funds for classrooms and programs. But that wasn’t the only reason: “We can break down this wall of racism that divides us and keeps us separated,” he said, according to court documents. “And we could create a new culture in our school system that’s going to unite us and unite our whole city.”