On an 11-0 vote, the council allowed developer Geoffrey H. Palmer to erect the span over Temple Street, joining two sections of his 526-unit Da Vinci development.
Palmer's company told the city it needed the bridge because transients living under the nearby 110 Freeway posed a threat to the health and safety of future Da Vinci tenants.
The Central Area Planning Commission rejected the bridge last month, saying pedestrian activity belongs on the sidewalk. But Councilman Jose Huizar pushed his colleagues to overturn that decision, saying Palmer had promised to provide $25,000 for upkeep of other downtown pedestrian bridges.
Huizar, who represents much of downtown, described the bridge as necessary for internal circulation -- allowing the Da Vinci's residents to move from one part of the project to another.
He said it was "unfortunate" that the bridge had been characterized as a way to avoid the homeless.
"Homeless encampments move all the time, particularly in this area of downtown Los Angeles, so it's not really a homeless issue," he said.
Palmer's company, G.H. Palmer Associates, said in paperwork filed with the city that it requested the bridge "specifically because it is concerned about the safety of project residents and potential incidents that could occur during the evening hours when the homeless population is more active in the surrounding area."
That message drew sharp criticism from activists and architects who contend that Palmer is vilifying the homeless and turning his back on the street.
But downtown business groups defended him, saying he is constructing apartments in locations where other developers fear to build.
City planners rejected the bridge in February, saying it conflicts with downtown design guidelines and could make the sidewalk less safe by drawing people away from the street. Palmer filed an appeal, saying Temple Street will not become safer simply by forcing tenants to "use the street and interact with the homeless population."