The county wants to build a new headquarters complex on the site.
Architects, preservationists and tax watchdogs had all argued against demolition.
Some argued the building was an important piece of architectural history. It was designed by famed architect Marcel Breuer.
But in the end, the county managed to convince the planning commission that the present building could not be adequately renovated to meet needs.
Demolition is expected to take place in the spring with a new building opening by 2011.
The building will house 1,700 county workers.
It’s hoped that the building will help revitalize Euclid Avenue.
Click play video for Tom Beres' story.