The nearly final but still unofficial results were released two weeks after the election and after previous attempts to release preliminary results were botched, leading to confusion and drawing criticism of the Board of Elections.
Tuesday's tabulation using the city's new ranked-choice voting system included absentee ballots for the first time, although some of the approximately 125,000 ballots remained uncounted.
Adams, a former police officer, led the city's former sanitation chief, Kathryn Garcia, 50.5% to 49.5% in head-to-head competition after the rest of the field was eliminated.
Civil rights attorney Maya Wiley had remained in the running, thanks to ranked-choice ballots, which allowed voters to rank up to five candidates in order of preference. But she was in third place in the latest results.
The winner of the Democratic primary will be heavily favored in November's election against Republican nominee Curtis Sliwa, the founder of the Guardian Angels civilian patrol, given that Democratic voters outnumber Republicans in the city by more than a 6-to-1 margin. Reporting by Joseph Ax; Editing by Bill Berkrot and Peter Cooney