The bill establishes a procedure for patients to request to end their lives. A second doctor would have to certify the original terminal diagnosis and confirm the patient is capable of making the decision to die without pressure from others.
Assisted suicide opponents have fought the measure.
A companion bill remains stalled in the state Senate. In the Assembly, it passed 41-31 on Thursday.
The vote comes weeks after physician-assisted suicide advocate Brittany Maynard ended her life under an Oregon law allowing terminally ill people to choose when to die.