The prohibition, which passed 13-1, will take effect over the next 12 months and will affect about 7,500 stores in the sprawling city.
While workers from companies producing the familiar sacks urged the council to kill the proposal, proponents said discarded bags were a litter problem and a threat to the environment.
"It is a threat to the coastal economy," H. David Nahai, a former top executive of the city's Department of Water and Power told the council. "It is a danger to marine life and it is an unconscionable burden to taxpayers who have to foot the bill for cleanups year after year."
The Los Angeles ban is similar to restrictions on bags in place in other California cities.
The Los Angeles Times said the banishment of plastic bags came at the same time the council appeared less enthusiastic about similar proposed limits on paper bags, which are aimed at reducing deforestation.