The city ordered the demolition after it found extensive deterioration making the structure "unstable and in imminent danger of failure or collapse."
Olmsted Parks Conservancy was behind the $230,000 restoration project to help separate the landmark from traffic.
The landmark sits on the park's Scenic Loop.
Following the vote, the roads are expected to reopen within the next few days.
Metro Council will consider the study's findings before voting on a plan in the coming weeks.
The loops closed to drivers at the start of the pandemic in an effort to help manage crowds.
Louisville Parks and Recreation hope to have a plan that can benefit everyone sometime in early May.
Louisville’s mayor announced in April 2020 the main roads through the popular local parks would be closed to vehicle traffic to help manage crowds.