“We have seen over the last week something amazing happened,” Mr. Caputo-Pearl said. “We took on the idea of bargaining for the common good. Public education desperately needs attention.”

The strike drew attention to how California, one of the wealthiest and most liberal states in the country, spends relatively little on its public schools. As they announced the outlines of the deal, Mr. Garcetti, Mr. Beutner and Mr. Caputo-Pearl declined to give specific details on how the district would pay for the changes, but school officials said that they would need more money from local voters and the state.

“We’re spending every nickel we have,” Mr. Beutner said. “It’s all in for schools. This is the start, not the end.”

Many of the changes — including class-size caps and full-time nurses at every school — would be phased in over time, officials said. Because those changes would occur over the next three years, the deal essentially punted on the question of how the district would come up with the $403 million needed to pay for the additional staff members. District officials said Tuesday that they expect to propose a local parcel tax in 2020, which would require the approval of two-thirds of voters in the sprawling school district. Mr. Beutner also made it clear that he expected the attention to now turn to Sacramento for increased funding.

The state’s chronically constrained school spending is largely attributed to its property tax laws, and especially to Proposition 13, a ballot initiative passed in 1978 that drastically limits tax rates and makes increases difficult to enact. Affluent, fast-growing suburban communities have suffered less under the law than large urban systems like the Los Angeles Unified School District, where declining enrollment and rising costs for pensions and health care have created budget problems year after year.

While many educators and local leaders have called the strike a watershed moment for California public schools, it is far from clear whether there is a political willingness to change the statewide property tax laws. The union and district officials are both backing a ballot measure that would increase taxes on commercial, though not residential, properties in 2020.

The strike settlement is also a significant achievement for the Mr. Garcetti, who has no formal authority over the school system. Though he publicly supported the teachers, he acted as a mediator of sorts and helped broker the deal during days of negotiations at City Hall. Before the strike, Mr. Garcetti had largely shied away from involvement with the public schools, but with the national spotlight on the strike and the mayor considering a presidential bid in 2020, he appeared eager to get involved during the past week.