Independent Municipality Flexibility, in San Francisco!

San Francisco has a new idea about where to house residents: basements and garages.

Grappling with a housing shortage that has sent rents soaring 50% since the recession, city officials on Tuesday passed legislation allowing landlords to carve fresh apartments out of underutilized spaces, including storage areas and utility rooms.

City leaders for more than a decade have tried to allow for new units to be tucked inside existing buildings, arrangements sometimes known as in-law units. Until now those efforts have been met with opposition from groups worried about overcrowding and parking shortages.

But with a growing sense of urgency about housing affordability, the San Francisco Board of Supervisors approved the measure. It next goes to the mayor, who was expected to sign it.

“The whole in-law unit conversation was long viewed as the third rail of San Francisco politics,” said Aaron Peskin, a supervisor who co-sponsored the legislation. “Whether it’s a shift in thinking or an adjustment to the crisis at hand, it is a sea change.”

The measure allows for buildings with fewer than five units to add one apartment and larger buildings to add unlimited units. City planners estimate that could add some 14,000 units to the city’s housing stock.

The increased supply is expected to help drive down housing costs. San Francisco added just over 3,000 housing units in 2015, down 15% from 2014. About 500 of those units were deemed affordable to low- and middle-income families, down from more than 750 affordable units built the year before.

The ad-hoc units, which will be rent controlled, also tend to carry lower rents than most apartments because they are often smaller and get less natural light. Still, some worried the legislation doesn’t account for parking or overcrowding.

“The proof will be in the pudding,” said Mike Antonini, a city planning commissioner. “It’s been rushed up very quickly because there’s this whole conception that we have this housing crisis.”

Cities across North America, from Vancouver to Cambridge, Mass., have been moving to encourage the creation of additional units to address shortages of affordable housing. The classic version of such spaces is a small, free-standing structure in a backyard, or a basement apartment in a single-family home.

San Francisco’s legislation is unusual in that it is designed to encourage the creation of units within apartment buildings as well as in single-family houses.

Doug Bibby, president of the National Multifamily Housing Council, a trade group for apartment landlords, said this is the first legislation his group has seen that allows for the creation of additional units tucked into existing apartment buildings in a tightly regulated market.

“When we see a municipality showing some flexibility to get more units that are affordable to people, we’re intrigued,” Mr. Bibby said.

Yat-Pang Au, chief executive of Veritas, one of San Francisco’s largest apartment owners, said the new rule will allow a greater diversity of tenants to remain in the city and also is a boon for landlords, who can make money from little-used spaces. The change, he said, “works well in terms of spreading diversity and also works economically.”