Commissioners said the demolition will help improve the east side neighborhood, 10TV's Tino Ramos reported.
The Poindexter Towers, on Mount Vernon Avenue, is now in the hands of a community group, which has plans to demolish it.
SLIDESHOW: Images From Building
The building has been vacant for about eight years.
Neighbors and the Central Ohio Community Improvement Corp. say the building has become an eyesore that is creating crime and holding back progress, Ramos reported.
"When we get to the endpoint, it's been a blight on the community for nearly a decade now," said Franklin County Treasurer Ed Leonard.
Owners of about 30 units still have to be notified of the plan, Ramos reported.
Then the community improvement corporation will file for a nuisance abatement, which will order them to tear down the facility.
Officials said it could be another year before the building sees a wrecking ball.
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