The Assembly approved the bill Wednesday on a 42-33 vote, sending it to the state Senate, which is expected to endorse it. Assembly lawmakers were seen as the stumbling block to advancing the bill.
The legislation would allow doctors to prescribe life-ending medication. It comes after the highly publicized case of 29-year-old Brittany Maynard, a California woman with brain cancer who moved to Oregon to legally take her life.
Democratic Gov. Jerry Brown, a lifelong Catholic, has not said whether he will sign the bill. He previously indicated he did not think it should have been considered during a special legislative session on health care.