The measures would ensure people buying insurance under the Affordable Care Act would not be denied because of a pre-existing condition.
One Republican Senator raised concerns about how the bill would increase insurance costs next year.
But one of the bill's authors says the measure would enable all Californians to have better access to health insurance.
The bill would allow insurance companies to charge premiums based only on age, family size, and geography.
The Governor has 12 days to act on the bills after his office receives them.