The bill was approved by the House early Monday with no debate, following Senate passage last week.
The measure allows abortion clinic employees, not just patients, to file complaints for investigations by the Department of Health and Social Services.
The bill, which now goes to Gov. Jack Markell, also requires abortion clinics to be accredited by a state-approved independent accrediting organization with no conflict of interest. Planned Parenthood accredits its own clinics.
The Planned Parenthood clinic was cited recently for several unsafe and unsanitary practices. Officials also filed a complaint against a doctor who performed abortions there, saying he was a danger to the public.