California will cap rent increases under a new law signed Tuesday by Gov. Gavin Newsom, the most significant piece of housing-related legislation in a year that also saw the shelving of a measure to relax zoning and spur more construction.

The Democratic governor has said the rent caps and tenant protections are necessary to help people being squeezed out of their homes. The law limits annual rent increases at 5%, plus the rate of inflation, and adds some barriers for landlords seeking to evict people.

Before...