Harvard University’s undergraduate admissions process doesn’t intentionally discriminate against Asian-American applicants, a federal judge ruled, a victory for the university that is expected to be appealed as high as the Supreme Court.

In a 130-page ruling on Tuesday, U.S. District Judge Allison Burroughs found that Harvard’s practices were “not perfect” and could use improvements, including implicit bias training for admissions officers, but said “the Court will not dismantle a very fine admissions program that passes constitutional...