The bill was among dozens lawmakers approved as they rushed to meet a midnight deadline before the end of the current legislative session.
The health care bill "will make quality health care available to each of us while preserving our freedom of choice as consumers and patients," the bill's author, Democratic Sen. Sheila Kuehl, said after the Senate agreed to Assembly amendments on a 24-12 party-line vote.
Under the amended bill, California residents essentially would pay their health insurance premiums, copays and deductibles into a state-funded health insurance program. Money the state spends on health care also would go into the new system.
Kuehl, D-Santa Monica, modeled her bill on a private study that found billing each resident and business an annual premium based on income would be enough to pay for universal health care.
Kuehl said her bill guarantees that patients can choose their own doctors and would allow the state to cut prescription drug costs by negotiating bulk purchases. It also would help cut health care costs through increased efficiencies and reduced administrative costs, she said.
Her bill is opposed by the insurance industry and legislative Republicans, who have said it amounts to socialized medicine.
Schwarzenegger has said he opposes so-called single-payer health care systems.
In April, Massachusetts passed a plan that would require all residents to buy health insurance or face legal penalties, in much the same way California requires motorists to buy auto insurance.
Census figures show Californians are more likely to be uninsured than residents of other states, said Anthony Wright, executive director of Health Access California. The Legislature's approval of Kuehl's plan shows that California's health care system needs immediate improvement, he said.
Here are some other measures the Legislature voted on Thursday:
The bill by Senate President Pro Tem Don Perata, D-Oakland, would make the information available to public health planners.
Supporters detected dangerous amounts of toxic chemicals such as mercury and the pesticide DDT in the bodies of actor Peter Coyote, newspaper columnist Steve Lopez and other prominent Californians as they promoted the bill this year.
AB1835 by Assemblywoman Sally Lieber, D-San Jose, would give California the nation's highest minimum wage.
The legislation would give more than 1.4 million minimum-wage earners an increase of 75 cents an hour in January and another 50 cents the following year.
The Assembly voted 43-28 for the bill, with most Republicans opposing it. They said it would harm businesses and lessen people's motivation to finish high school and learn a trade.
It now goes to Schwarzenegger, who has said he will sign it.
Several studies have linked cell-phone use to traffic accidents.
The bill, SB1613, would authorize a $20 fine for a first offense and $50 for subsequent violations.
Calls made to 911 would not be covered by the bill.
The Republican governor and Democratic legislative leaders agreed the state needs a separate public health agency to deal with threats such as the West Nile Virus, bird flu and bioterrorism. The bill, SB162, is authored by Sen. Deborah Ortiz, D-Sacramento.