Much of the debate here has centered on potential regional repercussions. Many of the low-wage workers who form the backbone of Southern California’s economy live in the suburbs of Los Angeles. Proponents of the wage increase say they expect that several nearby cities, including Santa Monica, West Hollywood and Pasadena, will also approve higher wages.

But opponents of higher minimum wages, including small-business owners and the Los Angeles Chamber of Commerce, say the increase approved Tuesday could turn Los Angeles into a “wage island,” pushing businesses to nearby places where they can pay employees less.

“They are asking businesses to foot the bill on a social experiment that they would never do on their own employees,” said Stuart Waldman, the president of the Valley Industry and Commerce Association, a trade group that represents companies and other organizations in Southern California. “A lot of businesses aren’t going to make it,” he added. “It’s great that this is an increase for some employees, but the sad truth is that a lot of employees are going to lose their jobs.”

The 67 percent increase from the current state minimum will be phased in over five years, first to $10.50 in July 2016, then to $12 in 2017, $13.25 in 2018 and $14.25 in 2019. Businesses with fewer than 25 employees will have an extra year to carry out the plan. Starting in 2022, annual increases will be based on the Consumer Price Index average of the last 20 years. The City Council’s vote will instruct the city attorney to draft the language of the law, which will then come back to the Council for final approval.

The mayor of Los Angeles, Eric Garcetti, a Democrat, had proposed a slightly different increase last fall and later negotiated the details with the Democratic-controlled Council. Mr. Garcetti said Tuesday that he would sign the legislation and that he hoped other elected officials, including Mr. Cuomo, would follow Los Angeles’s path.