Under the changes, abortion will be treated as a healthcare issue, not a criminal one, in line with other states including Victoria, Queensland and NSW.
It can be performed by one medical practitioner up to 22 weeks and six days gestation.
After that time, a medical practitioner can only perform an abortion if they consult with another practitioner and if both are of the view that the procedure is medically appropriate.
Those circumstances could include if a life is at risk, if there's a serious foetal anomaly or a serious risk to a patient's physical or mental health.
Attorney-General Vickie Chapman said the passage of the legislation was a "historic day for the women of South Australia".
"It's been a long and, at times, ugly journey, but finally we have modern termination of pregnancy laws, which make abortion a health issue, not a criminal one," she said.
"This legislation makes explicit the higher standard of medical care and decision making that already exists in South Australia."
Advocacy group Fair Agenda said the bill was an important step towards ensuring everyone could access the healthcare they needed, when they needed it and where they needed it.
"A patient might need to end a pregnancy for any number of deeply complex and personal reasons," spokeswoman Renee Carr said.
The bill was subject to a conscience vote in both houses with MPs opposed to the legislation successfully securing a number of amendments.
These included a ban on sex-selective abortion and a requirement every patient be provided with information about counselling, regardless of their situation.
While opponents to the legislation remained concerned with provisions allowing for late-term procedures.
The Human Rights Law Centre said the passage of the bill in SA means only Western Australia still uses criminal law to regulate abortion.
"It is time for the Parliament of Western Australia to follow in the footsteps of South Australia and bring their laws into line with every other jurisdiction in the country by removing all barriers to timely reproductive healthcare," spokeswoman Monique Hurley said.