Massachusetts Gov. Charlie Baker signed into law the nation’s toughest prohibition on flavored tobacco, including a ban on menthol cigarettes.

The new restrictions will put Massachusetts at the forefront of a national crackdown on flavored tobacco in an effort to stop young people from developing tobacco habits. At the federal level, White House support for a ban on sweet and fruity e-cigarettes appeared to be softening after President Trump last week said a prohibition could have dangerous consequences.

“The bill we signed today goes a long way toward restricting access to the most addictive kinds of nicotine and vaping products,” Mr. Baker, a Republican, said during a signing ceremony at the statehouse.

He was flanked by advocates, health regulators, bill sponsors and leaders from the Democratic-led legislature, which passed the flavor-ban earlier this month.

A ban on flavored vaping products is slated to start immediately. Menthol cigarettes will be banned starting June 1. The bill adds an excise tax for unflavored vaping products, which are still allowed under the law but face new sales restrictions based on nicotine content, and expands access to smoking-cessation help.

The flavor ban doesn’t apply to places like cigar bars where people consume tobacco on site.

Mr. Baker had cracked down on vaping products in September by enacting a comprehensive-but-temporary sales ban in response to a nationwide outbreak of vaping-related lung injuries.

That ban was controversial with vape-shop owners and the vaping industry and sparked lawsuits against the state. The governor also said Wednesday he will end the ban on Dec. 11, a couple of weeks ahead of the most-recent scheduled end date, and that the state’s public-health department is working on new vaping regulations.

“Unfortunately it’s becoming increasingly clear the federal government is not going to act decisively, so we’re going to do everything that we can,” the governor said.

The permanent flavor-ban legislation placed Massachusetts on a national stage, and tobacco-control advocates hoped the new law would spur similar crackdowns elsewhere. Former New York City mayor and Democratic presidential candidate Michael Bloomberg called the Massachusetts law a model for the nation and had urged Mr. Baker to sign the bill.

“Today, Gov. Baker signed a legislative package that simply raises the bar for tobacco control across the country,” said Harold Wimmer, chief executive at the American Lung Association, in a statement.

The Vapor Technology Association, a trade group for the vaping industry, claimed the Massachusetts law won’t protect youth but will make life harder for adults trying to quit smoking.

A spokeswoman for British American Tobacco PLC unit Reynolds American Inc., a major maker of menthol cigarettes, said the company was considering going to court to fight the new Massachusetts law because it believes federal law governs which flavors should be permitted in tobacco products.

“We are evaluating our options, including a legal challenge,” spokeswoman Kaelan Hollon said.

State Attorney General Maura Healey said at the bill-signing event, “We will happily continue to defend any challenges to this or future laws.”

Convenience-store owners also pushed back, saying the new law would hurt sales and could drive some shops out of business. They focused their objections on the menthol-cigarette ban, which will wipe a product off store shelves that had escaped a federal crackdown on flavored cigarettes a decade ago.

Mr. Baker said he understood the state-level tobacco crackdown could impact businesses.

“I happen to believe the positive consequences of this one outweigh the negative ones,” he said.

John Kamp/Wall Street Journal