So called "vaping" lounges and stores will be exempted, in line with exceptions made for cigar and hookah lounges where tobacco smoking is allowed, as will using e-cigarettes for "theatrical purposes."
The battery-powered devices, marketed as aids to quit smoking, allow users to inhale a nicotine-laced vapor, but experts say not enough is known about the effect of chemicals involved, on smokers or those around them.
"Safer does not mean safe," said the LA County's public health director Dr. Jonathan Fielding. "Although they are less harmful than traditional cigarettes, some e-cigarettes contains some health risks."
He added that e-cigarettes have grown into a "$1.5 billion industry that has caught the attention of big tobacco which historically has had scant regard for public health."
LA mayor Eric Garcetti still has to approve the ban for it to come into force.
The LA vote follows a similar move last December in New York City, which agreed to extend its strict smoking ban to e-cigarettes, barring them from bars, restaurants, parks, beaches and other public places.
The industry has exploded in the United States, doubling turnover in one year to $1-1.7 billion at the end of last year, according to financial group Wells Fargo last year. Sales grew ninefold between 2010 and 2012, studies suggest.
Regulation varies from state to state in the US, but they are often banned from sale to minors, and they are not allowed on planes or trains.
- US is studying the device -
On a federal level, the US Food and Drug Administration (FDA) is studying the devices, but regulation by the agency could "take years to do," said University of Southern California (USC) professor Lourdes Baezconde-Garbanati.
Most worryingly for some are e-cigarettes flavored like bubble-gum or fruit, marketed specifically at young people.
"I am most concerned about kids," said city lawmaker Paul Koretz, co-sponsor of the ban. "We all know this is being marketed to kids, getting some kids who don't smoke tobacco to start."
A proposal to exempt bars from the ban was narrowly defeated, on an 8-6 vote.Council member Joe Buscaino, who supported the right to use e-cigarettes in bars, said: "Although e-cigarettes look like cigarettes, they are not tobacco, and I don't think they should be regulated exactly the same way.
"I've heard from so many people ... that they've stopped smoking because of e-cigarettes," he said.
In Europe several countries -- including Belgium, Luxembourg, Malta, Slovenia and Lithuania -- e-cigarettes are banned wherever tobacco smoking is banned. Some states, including Italy and France, outlaw sales to minors.
E-cigarettes are banned in several Latin American countries, while in Asia there is relatively little interest in countries where tobacco is cheap including China, where the devices were invented.