The House on Friday passed the Senate’s tobacco bill and sent it to the White House, where President Obama promised to sign it quickly.

Obama, who has struggled to quit smoking, said the measure would “protect our kids and improve our public health.”

The law would, for the first time, give the Food and Drug Administration (FDA) the authority to regulate tobacco products, which kill more than 400,000 people in this country each year, according to the Centers for Disease Control and Prevention (CDC). In addition, $100 billion in health-care costs are attributed every year to smoking in the U.S.

The House vote Friday was 307-97 and followed Senate passage of the measure 79-17 on Thursday. All members of the Washington delegation voted for the measure, except Republican Doc Hastings, who did not vote.

Under the law, the FDA will be able to set product standards and ban some chemicals in tobacco products, but not totally ban addictive nicotine. The FDA will set up a tobacco-regulatory office financed by industry fees, which are expected to be $85 million in the first year and as much as $700 million annually in 10 years.

The FDA would have the power to consider changing existing products and to ban new products unless the agency found they contributed to overall public health.

Within 15 months, the FDA is charged with imposing a ban on tobacco advertising within 1,000 feet of schools and playgrounds, a measure likely to draw court challenges from the tobacco industry, saying it violates the First Amendment.

Also, within one year, the industry will be banned from claiming products are “light,” “mild” or “low-tar,” terms that have been found to mislead smokers into thinking the products are safer when they are not.

The law provides that by 2012, new graphic warning labels must be designed and approved by the FDA and occupy 50 percent of the space on each package of cigarettes.

Seeking to combat youth smoking — Obama noted that an additional 1,000 or so Americans younger than 18 become regular smokers each day — the legislation will quickly ban most flavoring in tobacco and raise penalties for sales of tobacco to underage buyers.

In a political compromise it exempted one flavoring, menthol, which masks the harshness of tobacco and accounts for about one-quarter of the market.